Answer
$P=10rsin36^{\circ}$
Work Step by Step
When we break a regular pentagon into 10 separate right triangles, each triangle has an angle of 36 degrees in it. Using this angle and the fact that the radius is r, we find:
$sin36^{\circ}=\frac{s/2}{r} \\ s/2 = rsin36^{\circ} \\ s = 2rsin36^{\circ}$
Since there are 5 sides, we find:
$P = 5s = 10rsin36^{\circ}$