AMC 12 2013b Problem 6

Real numbers $x$ and $y$ satisfy the equation $x^2 + y^2 = 10x - 6y - 34$. What is $x + y$?

\textbf{(A)}\ 1 \textbf{(B)}\ 2 \textbf{(C)}\ 3 \textbf{(D)}\ 6 \textbf{(E)}\ 8