Answer
$r=4.3 cm$
Work Step by Step
We draw an apothem. Then, we draw a triangle that extends to a corner of the pentagon closest to the apothem. This means the angle created is:
$360/10=36$
We will call the apothem a. If we call the radius r, we can find:
$cos(36)=a/r$
This means
$r=a/cos(36)$
$r=4.3 cm$
