I'm going to be honest, and I do not know your situation fully, so you have to do what is best for you.
I would start him in kindergarten. Talk to the Kinder teachers, and find out if he meets the basic requirements. If he is acting up because he is bored, especially if he is bored because he already knows what he is doing, he needs more of a challenge. Unless the pre-k teachers can give thet to him, send him off to Kinder. My kid acts up when he is bored, or if he already knows simething, and his teacher realized this instantly-if he doesn't do all his work, he misses out on part of second recess (full day kinder-two recesses), and helps tidy the room. If he fineshes his work early, she has extra for him to do. He ate up and spit out the pre-k teacher, but we were leary of his social skills, and other things most kinder's posess. He has learned what he needs to interact with his peers in the manner befitting a polite five year old, and in his words "Is so happy to be learning at school ,not just home!"