This article is from the Puzzles FAQ, by Chris Cole firstname.lastname@example.org and Matthew Daly email@example.com with numerous contributions by others.
Can you dissect a square into 5 parts of equal area with just a straight edge?
1. Prove you can reflect points which lie on the sides of the square
about the diagonals.
2. Construct two different rectangles whose vertices lie on the square
and whose sides are parallel to the diagonals.
3. Construct points A, A', B, B' on one (extended) side of the square
such that A/A' and B/B' are mirror image pairs with respect to another
side of the square.
4. Construct the mirror image of the center of the square in one
of the sides.
5. Divide the original square into 4 equal squares whose sides are
parallel to the sides of the original square.
6. Divide one side of the square into 8 equal segments.
7. Construct a trapezoid in which one base is a square side and one
base is 5/8 of the opposite square side.
8. Divide one side of the square into 5 equal segments.
9. Divide the square into 5 equal rectangles.