Pedro Martínez: I'm more considering the infinite set of dice rolls as a fait accompli that we can just dip into and grab something out of. As the set already exists and it contains every dice roll sequence, then the 5-5... must be in there. 100%

As you head towards infinity, generating the 5-5s as you go, the probability shrinks by 1/36 each time and certainly tends towards zero. But when you eventually reach infinity (I know, lol, I know) then Hey Presto! the probabilities for all sequences suddenly jump to 100%! Strange things them infinities.

But I'm looking at it from a logical point of view, not that of a mathematician. Strange things them mathematicians. ;-)