Controlling output voltage (12v to 0-12v 5a)
You want a switching regulator with an enable pin. A step up or boost regulator,  or a step down buck regulator, depending on your input voltage supply. Most will have 80% or higher efficiency,  but you still need to make sure your input power supply can meet or exceed that. 12v 5A is 60W, so your input should be a 72W power supply. I'd go with a 6A regulator too because you don't want to push a 5A one to the limit.

The enable pin allows you to turn on and off the supply with digital logic.