Divide Paper into Fifths: Fujimoto Approx.
Interestingly, you can "eyeball" a 1/5 division and get surprisingly good results if you employ Fujimoto's Approximation. This method decreases the initial error by a half every time you make a fold. Although it is an approximation, the final result is often good enough to proceed with your origami folding.
 Start on the leftedge of the paper and make a pinch fold at a location which you estimate to be approximately 1/5th of the length of the paper.
Call this pinch mark "A".
 Fold the rightcorner of the paper so it meets with "A". Make pinch fold "B".
 Fold the rightcorner of the paper so it meets with "B".
Make a pinch fold "C".
 Fold the leftcorner of the paper to meet with "C" and make pinch fold "D".
 Fold the leftcorner of the paper to pinch mark "D". Press down to form crease "E". Assuming that your initial pinch "A" is not too far off, crease E will be quite close to the true 1/5th division.
 At this point, it is just a matter of folding the right side of the paper in half to get 2/5th segments.
These are then folded in half to get five 1/5th divisions.
Fujimoto's approximation works for any divisions and any angle too. The mathematics behind the Fujimoto Approximation is discussed in Tom Hull's book Project Origami: Activities for Exploring Mathematics. You can also learn more about this approximation here.
