5. For how many integers $n$ is $\frac{3 n}{n+5}$ an integer and divisible by 4?
(A) 1
(B) 2
(C) 4
(D) 8
(E) more than 8.
5. The answer is $\mathbf{( C )}$. Substituting $m=n+5$, the given expression becomes $\frac{3 m-15}{m}$, which is $3-\frac{15}{m}$. For this to be an integer, therefore, $m$ must be a divisor of 15, so the possibilities are only $1,3,5$, 15 and their
negatives. Of these, the only ones for which the expression is a multiple of 4 are $1,-3,5$ and -15, so the $n$ sought are $-20,-8,-4$ and 0.