2017 AMC 10B 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\qquad\textbf{(B)}\ -8\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}\ 8\qquad\textbf{(E)}\ 13

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.