Question 67
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 $f(a, b, c, d)$.