So I have two college kids who were both diagnosed as gifted in midschool but were never diagnosed with ADHD until college. Both did fine, competed in sports, did well enough in school without any effort and never triggered a concern from me. It wasn't until college with the classes were so much harder and time-intensive, their schedules so much more complex that they started to fail. Since being diagnosed, they both have gone from struggling to maintain grade levels high enough to not get kicked out of college to getting all A's and B's - in engineering.
My youngest has been tested twice and had ADHD ruled out despite having several of the symptoms. Disorganization, distraction, failure to sit still, impulsive interjections, etc. can all be attributed to so many other things besides ADHD.
At 5, he's also dealing with a racing mind from his high IQ and not being able to have his body keep up with his mind at times. That can cause a lot of what you're describing.
If he is failing in school or constantly getting in trouble, it would be worth seeing a qualified pediatric psychologist to express your concerns. But if he isn't failing, I personally would leave it a lone and just take note of the behaviors and see what makes them worse, better, when they go away or show up - and see if you see patterns. It will help you understand how to help your son better manage those situations and will also be very helpful should you decide to pursue a diagnosis.
