You can use DIVIDE to place 5 equally-spaced Point objects around the Circle, and then draw the pentagon using NODE Object Snap to the Points.
But I agree, POLYGON will do it directly, asking for 5 sides. If the Circle is already drawn, Osnap to its Center for the center of the pentagon, choose the Inscribed option, and Osnap to the top QUAdrant point of the Circle. But you don't need the Circle as a middleman if that's what it is -- if you know its radius, you can use that to place a circumscribing point relative to the center.
Kent Cooper, AIA