Let the radius of the fencing circle = R.

Let the radius of the circle circumscribing the pentagon = r

Then: R = r + 25.

So you have to find r. Any interior angle of the pentaon = 540/5=108.

Join center of pentagon (O) with 2 arbitrary vertices of the pentagon (let's say A and B)

Take aside triangle AOB, with OA=OB=r, angle A = angle B = 54 and side AB=92.5

Now drop the altitude from O, which will bisect AB at M.

Triangle OAM is right angled, with angle M = 90 degrees, angle A = 54 degrees, side AM = 92.5/4=46.25 and you can find the side OA (that is r) by using trigonometric ratios.

Once you have found r, you know R, and once you know R you can calculate the circumference of the fencing circle =