Well, I can't know for sure, but I have a distinct feeling that it's 5.
I mean I'm pretty sure unless I have some numbers for p and q theres no way.
So uhh, either gimme some numbers, or live with the fact that it's most likely 5.
Yay!
\(\text{GCF}(10p^2, 25pq, 15q^2) = \boxed{5}\)
To check, 10p^2/5 = 2p^2, 25pq/5 = 5pq, and 15q^2/5 = 3q^2, all of which have no factors in common.