Question 50
Compute the number of ordered quintuples of nonnegative integers $\left(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\right)$ such that $0 \leq a_{1}, a_{2}, a_{3}, a_{4}, a_{5} \leq 7$ and $5$ divides $2^{a_{1}}+2^{a_{2}}+2^{a_{3}}+2^{a_{4}}+2^{a_{5}}$.