I wouldn't start with the clean. Trade out a deadlift as your pull. When you stop making progress on the deadlift, alternate with the power clean.
It's a great idea to add overhead presses. You can alternate those with the bench, and you shouldn't need to do HLM, just add weight every session.
So it would be Squat/Bench/Deadlift on the first day and then Squat/Press/Deadlift on the second day. Just keep adding weight until you can't.
Also, final thought, 5x5 is probably too much volume right off the bat. Try 3x5 and see how that goes for a while.
I promise you will get stronger doing this and look good. Just get real strong.