So the answer is 1. because the length of the number zero is 1.

Or if you just want the length of 5^5000000000, that's easy enough too, with a little help from logs and a calculator:
5^5000000000=10^(log(5^5000000000))
=10^(5000000000*log(5))
5000000000*log(5)=3494850021.680094023931305526377 5

so the length of 5^5e9 is 3494850022