AHSME 1960 Problem 31

For $x^2+2x+5$ to be a factor of $x^4+px^2+q$, the values of $p$ and $q$ must be, respectively: $\textbf{(A)}\ -2, 5 \textbf{(B)}\ 5, 25 \textbf{(C)}\ 10, 20 \textbf{(D)}\ 6, 25 \textbf{(E)}\ 14, 25$