AMC 10 2017b Problem 10

The lines with equations $ax-2y=c$ and $2x+by=-c$ are perpendicular and intersect at $(1, -5)$. What is $c$? $\textbf{(A)}\ -13 \textbf{(B)}\ -8 \textbf{(C)}\ 2 \textbf{(D)}\ 8 \textbf{(E)}\ 13$