How to construct a pentagon

Start with a perfect circle.  Find the center, and draw a radius (a straight line between the center and the edge of the circle).  Call the radius R1.  This point on the circumference will be your first point of the pentagon-- call it P1.
Draw another radius perpendicular to the first one.  Call it R2.  Find the point halfway along this radius, and put a temporary mark there.  Draw a line between that mark and P1.  Call this line L1. 

Now, and this is the trickiest part to do without a ruler and protractor, draw a line bisecting the angle between the new line L1 and R2, and put another mark where it intersects R1.  You may have to read that sentence a couple of times, unless you consult the illustration I'm going to shamelessly crib off Wolfram MathWorld and copy below.

Next, draw a line from this new mark perpendicular to R2 out to the edge of the circle.  Where it hits will be your second point of the pentagon.  Call it P2.

Erase all of the incidental interior lines, and then repeat this sequence of steps three more times, each time using the new P point (and its associated radius) as your starting point.  Connect all the Ps, and you'll have a regular pentagon.

Of course, if you have the protractor you need to properly bisect the angle in paragraph three, you can just measure out the 72 degree angles you need for the points, but where's the fun in that?  Also, there's probably some way to bisect an angle without a protractor, but I don't know what it is.