Oh, and yes, I think a healthy little snack helps behavior. In the school system, some kids have written into their IEP's that they are to have a small snack break at some point in the day.
Use of food items in occupational therapy is actually quite common. Chewy and crunchy things are used for a desired effect on the nervous system. It is really fascinating.
And anecdotaly, I do much better with a snack break and protein is most satisfying. (smile)
It sounds like you are certainly trying with your boy. I think it is great the academic strides that he is making. I think one thing that really helps is consistency. Keeping rules very firm and never waivering from them. Also, following through is helpful. If you threaten something, such as if you shout, we will leave. Then he shouts---- you must immediately leave. That kind of thing. Then he knows you mean what he says. I'm also big on natural consequences. If you throw something, it is taken away for a time. There is a book called "sos for parents" by Lynn Clarke which really helps with the time out technique. You may be able to find it at the library.
I think little boys possess lots of energy. They need physical outlets for such. Try to work into his day many breaks for this. You can play physical games with him, set up an obstacle course, run races, crash into pillows, etc. He may get a little revved up during the activity but it has a calming effect afterwards.
As far as impulsive behavior. Well, 5 year olds are working on this. I talk to my kids about that we all have an on button that is pressed all the time. But we also have an off button that we need to remind ourselves to press. Getting a pause between impulse and action is good so whatever means you can do this is helpful. It comes more naturally starting at the age of 6.
Good luck and always be cooperative with school people as it makes for a team approach for handling any issues.
Food makes a big difference in my kids behaviour. Mainly Omega 3 (Udo's Oil) in a smoothie every morning, and a little protein every few hours, even just a couple of small bites of meat, a few nuts or a boiled egg. They argue less, are calmer, cope better, and more cheerful when I do this.
Especially if behaviour seems to be always at certain times of day, I would make sure they have that little bit of protein a half hour or so before it would usually happen. I clued into this when an adult friend of mine told me that he had noticed that he feels 'squirrly' if he doesn't eat a little protein every few hours, and sure enough, it worked for my kids too.
Hope these small ideas help you too, they are pretty easy.