gcd and lcm - GCD of two big numbers

How to find $gcd(5^{100}-1, 5^{120}-1)$?
The problem is numbers are really big ($5^{100}$ is 70 digits). None of the numbers is prime.
I ran Euclid's algorithm on Python and found the answer in less than a second, however it seems that there is no on-paper approach to this problem, is it?