Here I demonstrate how to draw a perfect pentagon. You will need a ruler and a compass. First draw the horizontal and vertical lines. Then draw the circle centered on the crosshairs. Do not fold the compass after the circle is drawn. The side of the pentagon will be 1.176 times the radius.
It may be difficult to lay out with standard drafting tools, but with the method below, you can draw one with just a compass and a straight-edge. Start off with a circle of a size that will perfectly fit your pentagon; that is, each corner of your pentagon will touch the outside of your circle.
A regular pentagon is a five-sided polygon with sides of equal length and interior angles of 108° (3π/5 rad). Because 5 is a Fermat prime, you can construct a regular pentagon using only a straightedge and compass.
Draw an arc with the compass from AG through to B, and the other way until it hits the side of the circle at C. Now we have three of the 5 points of the pentagon, A, B, and C.
In his book 'Underweysung der Messung' Durer draw a non-regular pentagon with ruler and a fixed compass. It is a simple construction and a very good approximation of a regular pentagon.