Hi and welcome.
I recommend taking him to a neuropsychologist or for a detailed evaluation by a group of professionals. Therapists are not trained to test and diagnose.
In the meantime, you may want to purchase "The Explosive Child" by Ross Greene. It's helpful in the short term, but something is obviously not right and in my opinion t he earlier you find out what it is, the better. These problems do not tend to go away...they tend to get worse with age if not taken care of. Violence can get him into a lot of trouble, however most of our kids do not respond to typical discipline. You need to find out what is "off" and your best bet is a neuropsychologist or multiple team evaluation (usually done at university or children's hospitals). At five you probably won't get the 100% answer, but you will at least be guided in some direction. Right now, you don't have a direction.
This is not your fault and has nothing at all to do with your parenting. Glad you found us, but sorry you had to. Can you give us a detailed background on him and tell us if there are any neurological or mental health issues on either side of his biological family tree?