smc

Let $x^2+y^2=r^2$, so $r=\sqrt{x^2+y^2}$. Thus, this problem is really finding the shortest distance from the origin to the line $5x+12y=60$. From the graph, the shortest distance from the origin to the line is the altitude to the hypotenuse of the right triangle with legs $5$ and $12$. The hypotenuse is $13$ and the area is $30$, so the altitude to the hypotenuse is $\frac{60}{13}$, which is answer choice $\boxed{\frac{60}{13}}$.