HMMT 2015 U12

For integers $a, b, c, d$, let $f(a, b, c, d)$ denote the number of ordered pairs of integers $(x, y) \in$ $\{1,2,3,4,5\}^{2}$ such that $a x+b y$ and $c x+d y$ are both divisible by 5 . Find the sum of all possible values of $f(a, b, c, d)$.