Permutations and Combinations: JEE Main 2026 Mathematics question

Let $S=\{(m,n):m,n\in\{1,2,3,\ldots,50\}\}$. If the number of elements $(m,n)$ in S such that $6^m+9^n$ is a multiple of 5 is p and the number of elements $(m,n)$ in S such that $m+n$ is a square of a prime number is q, then $p+q$ is equal to ______.