AMC 12 2018b Problem 17

Let $p$ and $q$ be positive integers such that $$\frac{5}{9} < \frac{p}{q} < \frac{4}{7}$$and $q$ is as small as possible. What is $q-p$?

$\textbf{(A) } 7 \textbf{(B) } 11 \textbf{(C) } 13 \textbf{(D) } 17 \textbf{(E) } 19$