Proof Writing & Problem Solving · Superchallenge problem

Each of $a_1, a_2, \ldots, a_6$ is chosen from $\{1, 2, 3, 4, 5\}$ (repetition allowed). For how many of the $5^6$ choices is $a_1^4 + a_2^4 + \cdots + a_6^4$ divisible by $5$?