Distinct points $P$, $Q$, $R$, $S$ lie on the circle $x^2+y^2=25$ and have integer coordinates. The distances $PQ$ and $RS$ are irrational numbers. What is the greatest possible value of the ratio $\frac{PQ}{RS}$? $\textbf{(A)}\ 3\qquad$ $\textbf{(B)}\ 5\qquad$ $\textbf{(C)}\ 3\sqrt{5}\qquad$ $\textbf{(D)}\ 7\qquad$ $\textbf{(E)}\ 5\sqrt{2}$