I have an extremely impulsive 15 yo son. When he was 5 1/2 it only presented in public places. When school called I had no idea what they were talking about. We have over the years learned that he has sensory issues and his impulsivity peaks when he is over stimulated. Perhaps you could recommend an OT eval? It wouldn't hurt!
I wish I had known what an OT was when he was 5. Would have saved us a world of heartache over the years.