X5's story is very tricky because it can go many ways. Thus, this summary will go all over the place as well. Try to stay with me, I did the best I could.
Life has been good on planet Earth, which is a catalyst for trouble. Under the pay of Sigma, a neato reploid bounty hunter named Dynamo diverts the space colony Eurasia from its orbit, and sends it on path to smack into earth. The Hunters panic, and decide something had better be done, and damned quickly.
Two options are available. The first is a giant but ancient cannon called The Enigma. But for the shot to be successful, X and Zero must collect bits of things to re-enforce the old weapon. Thus begins the battle with the first four "Mavericks."
NOTE: Not all the parts have to be collected before firing the Enigma, but it increases your success rate greatly. Keep in mind, however, that even all the parts don't guarantee success! Failiure will lead to the Space Shuttle option, and the next four Mavericks.
If the crew succeeds in destroying the colony, we learn about the Zero virus--a more lethal version of the Sigma virus. Its origins are in what appears to be a destroyed lab of Dr. Wily's!
Zero begins to realize there's something mighty funny about his structure. When infected with the Maverick Virus, he doesn't degenerate--on the contrary, he feels great. And Lifesaver, the Hunters' medic, notices this as well as Zero's negative reaction to the virus' vaccines. He reports it to Signas, the new leader of the Hunters. Signas tells Lifesaver to keep an eye on things.
Which Lifesaver does. Zero enters and explores the wrecked lab a bit (don't you love the music here?) which is crawling with the virus. Eventually, X touches down with Lifesaver in tow. X is now mighty suspicious of his friend, and urges him to return to base for a complete physical. Zero refuses, and the two fight it out.
Sigma comes across the two wounded warriors, and takes a shot at X. Zero saves X yet again, and Sigma challenges the Red one. Zero answers and prevails.
For whatever reason, Capcom decided to forgo the traditional "adjective/animal/extra points for alliteration" routine for naming their Mavericks, and did a hell of a thing--they named the Mavericks after Guns n Roses band members.
Nobody can really explain why. I'm going to say it's because GNR is extremely popular in Japan and CoJ figured we could all share in a joke. Too bad not many fans appreciated it. Some of them are so anal about the GNR names, they'll flip if you say "Dark Dizzy" instead of "Dark Necrobat."
Myself, I don't really care. And I get tired of watching people get so uptight. The game plays the same, and "Duff McWhalen" is a great name for a fake ID. Sometimes I use the Jap names. Sometimes I use the US ones. But don't tell me that one is right and the other is wrong cuz I'll whap yer face in. If it means that much to you, here's a dime. Go buy a life. I don't get it! Duff McWhalen is a whale! With feet! And people go on about how the NAME is stupid.
There's also been a lot of uneducated GNR bashing among MM fans since the game came out. It's fashionable to hate GNR because of something they had no involvement in. Since I still like the band a lot, I tell these people to shut up and go back to spinning their N*Sync records.
The game also took hits from "fans" because it featured still frames instead of anime. The still frames were drawn beautifully by Sensei himself, but we all know that 13-16 year olds think anime of ANY kind is God's gift to the world, even if it's grainy and ugly. Honestly now. When Zero went Maverick, could you imagine how badly voices would've spoiled the drama?
I didn't care for the way a lot of levels were rehashes of X4's, like Grizzly Slash's stage. It was bad, even for a Megaman game. And what the hell happened to the Skiver's sprite? Storm Eagle was better animated than that. But the music was great. No, the music was incredible.
Overall, a good game with much undeserved controversy. But I prefered X4 and X6.