Deauthorizing and reauthorizing a computer

I recently purchased a MacBook Pro. I have 2 iPads, my phone, and my two old pc’s authorized to play my music. I tried deauthorizing one of my iPads but I still can’t get my MacBook authorized in iTunes. I get an error saying I have reached my 5 device limit, even though I deauthorized one of them. I’m tempted to deauthorize all of them and then reauthorize them one by one. But, I’m not sure if it will allow me to reauthorize a device after deauthorizing it. Help!