1997 AHSME Problem 17

A line x=k intersects the graph of y=\log_5 x and the graph of y=\log_5 (x + 4). The distance between the points of intersection is 0.5. Given that k = a + \sqrt{b}, where a and b are integers, what is a+b?

\textbf{(A)}\ 6\qquad\textbf{(B)}\ 7\qquad\textbf{(C)}\ 8\qquad\textbf{(D)}\ 9\qquad\textbf{(E)}\ 10

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