Explanation: Due to Rome's longevity and its wide reach, there are a number of dates that can be used as its fall - some quite, uh, interesting. For bonus points, my date of choice isn't here.
Oh, and for those curious, the most commonly accepted answers are:
476 AD (Fall of the city of Rome and the Western Empire)
1204 AD (Sack of Constantinople and the break of government continuity in the Byzantine Empire)
1453 AD (Siege of Constantinople and conquest of the Byzantine Empire by the Ottoman Turks)
Woolly mammoths walked the Earth while the pyramids were being built (well, one small corner of it).
Oxford university was teaching before the Aztec Empire began.
I think I read through an entire AskReddit thread of these. A few I came across on my own and was surprised by: Fibbonacci of the numbers fame could have met Ghengis Khan, Benjamin Franklin could have talked to Isaac Newton, and Galileo was literally the same age as Shakespeare.
284 AD. The ascension of Diocletian and the shift away from the city of Rome as the center of the Empire. There's still an Empire after that point - but it's only dubiously Roman.
Dominate vs. Principate.
Coinage also took a steep nosedive in terms of quality and silver content at this point. I'd argue that Diocletian's argenteii were among the last really "good" coins produced before it all devolved into tiny pieces of copper (nummi). Then again, they were arguably more comemmorative than meant for circulation which is why you'll be fairly hard pressed to come across visibly worn ones.
Things got pretty chaotic in the 300s already. The battle of Adrianople or generally the Gothic War would be a classic choice, and you could even cut it off with Constantine or Valerian if you want to emphasis the transition to Christianity and the accompanying cultural shift.
I don't know why I'm guessing, PugJesus is right here...