T.S.
There is no age requirement to become pope. The Cardinals at the conclave choose the Pope. Truthfully, though, (not to correct pp) even being a Cardinal is not a REQUIREMENT. Any confirmed, Catholic man CAN be elected Pope. The tradition, however, is that he is chosen form the Cardinals themselves (for lots of reasons including the fact that it's unlikely that enough of them would KNOW enough about another rman). The Pope is typically older by virtue of the fact that Cardinals are older because they've been in the priesthood for quite some time before reaching that designation.
Another reason for the age of Popes is that the papacy is a lifetime position. Unless the Pope steps down (as happened recently, but almost never happens) you can't get a new Pope until the Pope dies... so (not to be morbid but) an older Pope allows for a new choice for frequently.
That being said, I'm much more interested in the Pope's view of the Church, and doctrine in the world than I am about the age of the man himself.
HTH
T.