It is always hard to draw a polygon (eg. decagons, nonagons, heptagons...etc) with compass and ruler. The method I discovered is to divide a polygon into smaller triangles. That means you only have to concentrate on one intersected triangle and the relations between the vectors. The other triangles are just repetitions.
Your challenge is how to find out the angle phi for other n-polygons (general knowledge: Trigonometry, Maths - Secondary School). I give you a hint in the following pdf for n-gons.
If you have the solution for phi, don't post it here, they have to solve for their own!
So let's get started how to fold the pentagon.
Step 1: The Crease Pattern
Red: valley folds
Blue: mountain folds
Black: cutting lines