To help you understand the history of Babylon 5, I've written up overview's of most of the major events in the Babylon 5 universe.

        This war took place in 1250 (approximately) between the remaining 'First Ones' and Minbari against the 'Shadows' (who were also called "the ancients"). The alliance succeeded in beating back the Shadows, who then went into retreat, leaving many of their ships hidden on worlds throughout the galaxy. The remaining 'First Ones' (except the Vorlons and a few others) leave the known universe, beyond the rim.
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        The first alien race that made contact with Earth was the Centauri Republic in 2150 (approximately). In return for trade agreements, the Centauri Republic gave the Earth Alliance access to their technologies, including "jump gate" technology. This advanced Earth's technology over a hundred years and allowed them to explore and expand out of the solar system to become a major power in the galaxy.
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        The Earth Alliance was expanding in all directions everywhere, trying to expand its 'sphere of influence' in the galaxy. There was one major race left which they had yet not had any contact with, the Minbari. In 2242 an EarthForce cruiser was sent out to find the Minbari and bring back any information that they can, though when they made contact with a Minbari cruiser, it had its gun ports open as there gesture of openness, respect and greeting. The Earth ships misinterpreted this and opened fire, killing the Minbari leader, Dukhat. Outraged by this unprovocated attack the Minbari embarked on a holy war against the humans. The Earth Alliance did not have a chance as they could not destroy any of the Minbari ships in open combat (only one ship was destroyed by John Sheridan when he mined an asteroid field and tricked the Minbari in with a distress call) and so the Minbari ships reached Earth to exterminate the human race. But on the brink of victory, they surrendered.
        At the time it was unknown why the Minbari surrendered seeing as they had already won. Later we find out that after examining a human (Jeffery Sinclair), they believed that Minbari souls were being born into humans, and that they were killing there own people. The war lasted from 2242 to 2248.
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        The Babylon Project was launched by the Earth Alliance President in 2249, after the Earth - Minbari war. Its goal was to create a place where humans and aliens could work out their differences peacefully, thus preventing another war based upon a misunderstanding. This is possible because a representative from each of the races live on the station.
        There have been five stations: The first Babylon station was destroyed during its construction when its infrastructure collapsed. The second station was sabotaged during its construction. The third station was damaged during construction by an explosion and was abandoned because it could not be repaired. The fourth station, the biggest and most expensive (parts of the previous stations were used in its construction) of the Babylon stations was completed in 2254, but vanished 24 hours after it became operational. Later we found out that Captain Sheridan, Jeffery Sinclair and a few others, go back in time to steal Babylon 4. Sinclair then takes it back in time to help in the last great war.
        Babylon 5 was created on a much smaller budget than Babylon 4 as money was very tight, but even then they ran out of money and had to get the Centauri and the Minbari to sponsor it so that it could be completed. Babylon 5 went online in 2256.
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        The Centauri Republic conquered the Narn at the beginning of the 21st century. The Narn welcomed the Centauri with open arms and the Centauri occupied them for a hundred and thirty years and strip mined the planet. The Narns were able to defeat the Centauri and remove them from their homeworld by learning their technologies and turning them against them. Though the Narn managed to remove them, the Centauri had turned Narn from a forest planet into a bleak and barren one.
        After a thousand years 'asleep' an ancient race millions of years old called, " The Shadows", awoke and offer their help to the Centauri. Using this help, in 2259, the Centauri attacked the Narn and easily conquer there homeworld again by devastating. The Centauri fired asteroids (a weapon which is banned by almost every civilized race) at the planet destroying the whole Narn infrastructure and pushing rocks and dust into the atmosphere, it will take about a hundred years for the dust to settle. After this attack, the Narns unconditionally surrendered.
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        An Earth Alliance ship goes to a seemingly uninhabited planet called Z'ha'dum in search of the remains of an ancient race that was thought to have once lived there. They then awake the 'Shadows', Z'ha'dum is their homeworld. The 'Shadows' then go about quietly building up their forces which they had hid on planets throughout the galaxy (one was found on Mars and also one was on Ganymede) This event happen in 2256 (approximately).
        Then in 2259, the Shadows (without revealing who they are) helped the Centauri defeat the Narns, they then encouraged them to expand. Thinking that no one could ever defeat them with the Shadows support, the Centauri begin attacking all of the League on Non-Aligned Worlds governments on their borders. Whilst this is happening the Rangers are building up their own fleet of ships for the forthcoming war under the command of Delenn and Captain Sheridan.
        In 2260, the Shadows then start to fight openly and nothing seems to be able to destroy any other their ships. Captain Sheridan then discovers that telepaths can stop / confuse the Shadow ships (as they have human pilots). An alliance, the army of light, is made between of the Rangers, the League of non-aligned worlds, the Narns and the Minbari. They begin to attack the Shadows and using telepaths they manage to destroy a lot of Shadow ships, but for every ship the Shadows lose, the alliance lose two...
        Sheridan then goes to Z'ha'dum and nukes one of their major cities. The Shadows fall back to regroup.
        In 2261, things went from bad to worse as the Vorlons, seeing an opportunity to defeat the Shadows, started an offensive campaign to remove all traces of the Shadows from the galaxy. They showed no mercy, destroying entire worlds that had supported the shadows in any way, even if the Shadows had forced themselves on the planet. The Shadows respond by devastating worlds that had supported the Vorlons, but the Vorlons and Shadows continued to avoid directly battling each other...
        Captain Sheridan, realising what is really behind this, manages to trick them both into meeting each other in battle, hoping to force a definitive showdown. With the army of light and the help of the other remaining First Ones, who were angered by the Vorlons and Shadows behaviour, in reserve, they start to attack them both, even though there is no way that they can win.
        The First Ones were meant to be the 'Shepherds' of the 'younger' races, leading them to the way that they think they should act, but both of the Vorlons and the Shadows had different ideas of how this should be done. Being confronted by the united fleet of the younger races, the Vorlons and Shadows attempted to force Sheridan to choose one of their two approaches to growth and evolution; either the Shadow's way of 'chaos' or the Vorlons way of 'order'. Sheridan rejected both choices saying that the younger races didn't need shepherding any more, and would never again act as pawns, caught in the fight between them. The Shadows and Vorlons, convinced that their battle for ideological dominance could no longer continue because they had been rejected by the younger races, departed for the Rim, accompanied by the last of the remaining First Ones.

        At the end of 2258, with the death of the Earth Alliance President, Luis Santiago when the EA ship, EarthForce 1 exploded with him onboard, the vice President William Morgan Clark was sworn in as president. He implemented some 'Pro Earth' policies which included the group, 'Nightwatch'. The members of NightWatch were to find all anti-Earth speakers (even people just saying that some Earth policies are bad) and arrest them.
        In 2260 it was found that Clark asked the Shadows to destroy EarthForce 1, thus making him president, after this, he declared marshal law with the convenient excuses that a new alien race was attacking people and they need to defend themselves properly.. Several Earth colonies, including Mars did not want to implement this order and so Clark sent his forces in and attacked the Mars civilians.  After the attack on the Mars civilians, Babylon 5 declared its independence from Earth until Clark is removed from office. Clark then sent his forces to Babylon 5 capture it, but with the help of the Minbari, Babylon 5 repulsed the attack and became on independent state.
        In 2261, after the unprovoked attack on two unarmed civilians transports by Clark's forces killing hundreds of people, Captain Sheridan decided to attack back, by helping free Proxima 3 of Clark's forces blockading them. Sheridan then took those Earth ships that wanted to join him, and started attacking Clark's forces elsewhere. Along the way more and more Earth ships joined Sheridan against President Clark.
        Sheridan wanted the Earth Ship's to join him so that they were the ones leading, instead of the aliens attacking Earth, which the people would not like or support as they may think that they were being invaded or attacked again like in the Earth - Minbari War.
        Sheridan then was ready to strike at the forces at Mars, where Clark had gather a huge fleet of ships. But by using some technology that they had recovered from the Shadows, Sheridan managed to disable most of the ships on Mars and then disabled their weapons and engines. Sheridan's fleet then went immediately straight to Earth. He announced his arrival at Earth and then asked for the people to rise up against Clark, saying that he could not fight back as his ships have been drawn away from Earth. Sheridan then started to take out Earth's defence grid which was starting to firing upon his ships on Clark orders. With Sheridan's fleet destroying the defence grid, and his arrest imminent, Clark turned the defence grid to fire on Earth, to level it. He then took his own life. With the defence grid turned upon Earth charging up to fire, Sheridan called upon Delenn's Minbari fleet to aid in the attack and they manage to destroy all of the defence platforms.

        With the ending of the Earth Civil War, the interstellar alliance was created and John Sheridan was voted in to be its President. Its included the Minbari, the Centauri, the Narn, the League and Non-Aligned Worlds and the Earth Alliance (after they were offered some Minbari technology in return). The alliance had a set of principles and would help each of the other member races with trading and wars, though it would not interfere in the policies of each of the governments
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        With the Shadows gone, they left behind their allies, who took any of the Shadow technology they could find and left Z'ha'dum before it self-destructed. As the Centauri destroyed the Shadow fleet on Centauri Prime and executed their representative, the Drakh (a Shadow ally), wanted revenge.
        They took control of the Centauri regent by the use of a 'keeper' and ordered the construction of huge fleets of Centauri warships which were to be controlled remotely with the use of some Shadow technology. Controlling these fleets, the Drakh attacked the alliance shipping lanes everywhere, whether they were carrying materials or people, they left nothing alive. The alliance eventually found out that the Centauri were the one's attacking them, the Centauri denied this and withdrew from the Alliance.
        Without really knowing why the Centauri were attacking them for no particular gain, a Narn and Drazi (a league race) fleet jump to Centuari Prime and begin to devastate the city's. Just before the attack the Centuari Prime minister tells Londo that the Drakh ordered him to turn off the planetary defence network and to tell the Centuari home fleet to leave. The prime minister then goes on to say that he will be killed very soon and Londo will be made emperor. He also says that Londo can blame the Centuari attacks on the shipping lanes on him, saying that he was mad. The prime minister's keeper then leaves his body and he dies. The Drakh order Londo let them put a 'keeper' on him, he initial declines, but when told that if he does not the Drakh will explode bomb's all over Cenaturi prime which will kill millions his people, he let's the keeper attach it's self to him.

As the Centauri homefleet return and are about to attack the Narn and Drazi, Londo orders them to stop, ending the war.

The Centauri stay out of the Interstellar Alliance.
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        The telepath war takes place in 2264/5 which is after the events in Babylon 5 and before the events in Crusade. So we don't know yet what has happened but we will found out in the Crusade series.