I am not clear as to what you want explained. The chopper board can work with your motor.
Do you also understand that this chopper board only works with the unipolar board? In other words, this chopper board only replaces the power resistors for the unipolar board.
For a 3-axis system, your power supply can work. However, the work power required is determined by how fast and how hard you are cutting something. Hence I can't tell you what power you will be using. So it is possible that for some of your work you may need more current from your power supply than 5amps. For now just try it, if you already have the parts.
Also read the wiki... 3axis - PMinMO.com for further explanations.