AMC 10 2014a 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? $\textbf{(A)}\ {-20} \textbf{(B)}\ {-18} \textbf{(C)}\ {-15} \textbf{(D)}\ {-12} \textbf{(E)}\ {-8}$