hmm....
5 squared is 25. 25 x 25 is 625 which is 25 squared.
SO, look at it this way
5² + 5² = same bases, so you add the exponents together to get 5^4
5^4 can be rewritten as (5²)² which is equal to 25²
This is a perfect square.
Review the "laws of exponents" for more help. :-)