a) Assume $5$ does not divide $n$ and let the desired divisors be $a, b, c, d, e$. Then $n=a^4+b^4+c^4+d^4+e^4 \equiv 1+1+1+1+1 \equiv 0 (\mod 5),$ contradiction. b) Note that the number $42210$ satisfies, since $42210=2^4+3^4+6^4+7^4+14^4$. c) Note that if $n$ is good, so is $16n$, since $16n=(2a)^4+(2b)^4+(2c)^4+(2d)^4+(2e)^4$. So the set of good numbers is infinite.