"He also gets his way when tired." I suggest that you have to be consistent. By giving him his way when he's tired you're telling him it's OK to act that way. You have to consistently give him a consequence when he misbehaves.
My grandson was often out of control when a social worker suggested that she send/take him to his room to give him an opportunity to calm down. He could play while there which is allowing a tool to help him calm down. Send him to his room with the first sign of misbehavior before he's out of control.
Is he getting enough sleep/rest? Does he have 10-12 hours in bed at night? Quiet time in place of a nap should be OK. At 5, many children are not needing naps.
When you say quiet time, what do you mean? Is he in his room and unstimulated so that if he were tired he'd fall asleep?
At 5 he would be able to learn from talks. Check out some books from the library or get them from a book store about feelings and read them to him. During the reading talk about how to manage his anger.
Often, kids act out because they have sensory processing disorders and are anxious. It wold be a good idea to have him evaluated. You can do that thru the school district free of charge. Or you can start with his pediatrician.