Tekken 6 Storyline
Bryan entered The King of Iron Fist Tournament 5 to test his newly-acquired perpetual generator. However, time after time, Yoshimitsu got in the way of Bryan’s plans. In obtaining the perpetual generator, Bryan gained the potential for ultimate power but being unable to test it resulted in frustration.
Bryan could not contain his desire for destruction, so he traveled to the world's battlefields, wreaking havoc indiscriminately. He eventually grew tired of the comparatively weak foes he encountered, and craved a real challenge. Finally, The King of Iron Fist Tournament 6 was announced... Hungry for more capable prey, Bryan headed for the tournament to prove his mettle.
Source: tekken.namco.com
Tekken 5 Storyline
Bryan Fury, a replicant created by Dr. Abel, entrusted himself to Dr. Boskonovitch to recieve technological upgrades. Boskonovitch installed a prepetual power generator in the cybirg, Instead of thanks, Bryan killed severak people at the facility and then decided to enter the King of Iron Fist Tournament 5, thinking it the perfect test of his newky installed generator.

