2020 Fermat Problem 17

In the diagram, \triangle PQR is right-angled at Q and point S is on PR so that QS is perpendicular to PR. If the area of \triangle PQR is 30 and PQ = 5, the length of QS is

\textbf{(A)}\ \frac{60}{13}\quad \textbf{(B)}\ 5\quad \textbf{(C)}\ \frac{30}{13}\quad \textbf{(D)}\ 4\quad \textbf{(E)}\ 3

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.