5th Century -- that's the century in which to place the Roman Empire's fall in the year 476.
Historically, we've dated our calendars in the West according to the Christian calendar, with the approximate year of Christ's birth being the centerpoint. So "BC" years are "before Christ." AD years are (from Latin) - "Anno Domini" - "in the year of our Lord." The first century would be from year 1 to 100, second century from year 101 to 200, etc. So from 401 to 500 would be the 5th century.
In recent years, it has become common to refer to AD years as "CE" or "Common Era" and BC years as BCE ("Before the Common Era"), to take away some of the overt reference to Christianity in calendar dating.