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
Blue: mountain folds
Black: cutting lines