I have a little different take on what you've described. My son is a 6yr old w/ ADHD. I never would have gone that direction until I started researching it. He doesn't seem "distracted" to me. He can focus intently on what interests him but he most certainly does have it (we have physically WATCHED his brain showing the patterns in brain scans). Sensory issues and other stresses do make it worse and intense exercise makes it better.

Here's what I've learned that might be an explanation for your son's behavior:

ADHD brains crave stimulation. Their PFC (prefrontal cortex) is underactive and needs some adrenaline to "wake it up" enough to feel normal and okay. In fact TRYING to concentrate brings a REDUCTION in PFC activity in effect making it worse.

This makes mundane or non-stimulating activities extremely difficult to complete. Get your shoes on is a mundane task. Clean up toys, school work outside interest or challenge area, even following rules not very stimulating. It's painful in an ADHD brain to not have stimulation and they will seek it out sensory, relationally or otherwise.

Where can you get this stimulation? Conflict with others is an easy one. Time to play "Let's have a problem!" which is a favorite among the ADD crowd both young and old. How about waiting till the night before something big is due? The impending doom definitely amps up the adrenaline and suddenly gets the juices flowing.

The other part is moving moving moving for ADHD as well as being impulsive. Physical activity is phenomenally helpful. My little guy was running a mile each night before bed at one point when stress was so high just so he could go to sleep.

The impulsivity is part of the PFC shut down. PFC is the house for judgement/control/decision making and is not available or able to the ADHD thinker. It's just turned off sometimes and the result is not one that makes anyone feel good about behavior.

At school as you progress in grades teachers have expectation of increases in executive function, self control, initiating and completing tasks, and attention span for things outside your passion (rightfully so as this is developmentally appropriate in NT kids). All usually downfalls of ADHD kiddos. It looks like lazy, unmotivated, undisciplined, not applying yourself, and sometimes willful defiance to teachers. Report cards will show it and some teachers will openly display their displeasure with such a student creating even more problems for teacher/child and teacher/parent relationship.

Your child may have some completely different issue but if any of this is hitting home for you a good place to start reading is Dr. Daniel Amen's 6 Types of ADD. The preview is on Amazon. It really opened my eyes to something I thought I already knew about.