Chessmaster1000: How do you conclude that.......?

Trivial. Suppose you don't get an infinite number of finished games. Then there should be a finite number. Take the one which took the most moves, say R moves. But then your finite set of games didn't include the game that finished after R + 1 rolls of 5-5 by both sides. So, the assumption that there are a finite number of games is false.