2014 AMC 10A Problem 21

Positive integers a and b are such that the graphs of y=ax+5 and y=3x+b intersect the x-axis at the same point. What is the sum of all possible x-coordinates of these points of intersection?

\textbf{(A)}\ {-20}\qquad\textbf{(B)}\ {-18}\qquad\textbf{(C)}\ {-15}\qquad\textbf{(D)}\ {-12}\qquad\textbf{(E)}\ {-8}

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