List 5 types of action energy and 4 types of potential energy

Well, kinetic energy is defined as energy in motion (or as you said, action energy). Now, in order to characterize something as kinetic energy, it needs to be in motion (e.x., movement on a rollercoaster, a ball falling, a ball rolling, a person running, or a car in motion, really, anything moving).
Potential energy is stored energy. For example, it could be the farthest point back when you pull a slingshot. Or being at the very top of a hill right before you fall back down it, or holding a ball at its highest point before you drop it. Another example, is water stored behind a dam waiting to be released. Hope this helps!