Solution: The diagonal of the rectangle is the diameter of the circle. Using the Pythagorean theorem, the diagonal $d$ is $\sqrt5^2 + 8^2 = \sqrt25 + 64 = \sqrt89$. Therefore, the radius of the circle is $\frac\sqrt892$. The circumference is given by $2\pi r = 2\pi \cdot \frac\sqrt892 = \pi\sqrt89$. - Abu Waleed Tea