2021 AMC 10B Problem 9

The point P(a,b) in the xy-plane is first rotated counterclockwise by 90^\circ around the point (1,5) and then reflected about the line y = -x. The image of P after these two transformations is at (-6,3). What is b - a ?

\textbf{(A)} ~1 \qquad\textbf{(B)} ~3 \qquad\textbf{(C)} ~5 \qquad\textbf{(D)} ~7 \qquad\textbf{(E)} ~9

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