+678 Guest provided the correct answer but I expanded on it:
The formula for a cone's volume is \(V=\frac{1}{3}hπr²\) where h is the height and r is the radius. So let's plug what we know into that equation. The slant height is 13 and the radius is 5. If we use the Pythagorean theorem (\(a^2+b^2=c^2\)- where a, b, and c are the sides of a triangle), you find out that the third side of the triangle (or the height) is 12. So the radius is 5 and the height is 12 \(\Rightarrow \frac {1}{3}\times12\times\pi\times25 \Rightarrow 100\pi\) which is \(100\pi \space or \space \boxed{c}\).
