Fall of the Western Roman Empire: 476 AD
Final fall of Constantinople: 1453
...The last titular Roman Empire in the west, Romulus Augustulus, was deposed by the Germanic King Odoacer in 476, and this is widely accepted as the end of the Western Empire, though it had been effectively conquered and destroyed by Germanic invaders for some decades before that time.
The final end of the Eastern empire occurred when Constantinople was conquered by the Ottoman Turks under Sultan Mehmed in 1453. Only 4 decades before Columbus sailed to America. Although, again, it had been reduced to a position of prostrate weakness for some time before that year.