My son has been somewhat similar and has had sleeping difficulties as well. I think its all a vicious cycle. I don't think its 'normal' or good energy, I think its nervous energy. However, I would personally be loathe to label my son with all sorts of harsh sounding diagnoses like ADHD (and the harsh medications that go with them) without first of all trying a few little natural things myself.
How much sleep is your son getting each 24 hours? I read somewhere an average of 10.5 at night and 2 during the day for this age. If he's getting more, terrific, but if its less I'd personally look into that a bit more. In young kids, if they don't get enough sleep this can result in hyperactivity as they run on adrenaline the whole time, and paradoxically they actually need more sleep to be able to slow down.
I realized that my son was actually more frantic with his activity when he was more tired. I would notice that it wasn't quite so bad first thing in the morning, but got worse when he went 'past' the tired stage (past the time when he was rubbing eyes etc). We've had to work hard to help him to relax, and to relax more ourselves, as well as to be a better sleeper. I'm taking a mindfulness and meditation course which is helping me to relax more, and I've bought relaxation cd's for my son to listen to at nap time and sometimes right before bed. He can do that with whoever is with him and can relax by himself that way.
I won't go on too much about food and not letting him watch dvd's at mealtimes as others have already commented, but I think guiding him in these areas is a really important part of the process. It took some time, but we found stopping letting our son listen to audio stories at mealtimes meant that he was focusing more on his food. Encouraging him to sit still and eat rather than get up and down so much took time and patience as it didn't work straight away but has also helped. It seems he's eating more appropriate amounts as well - not too much and not too little.
I do find at times I actually need to hug my son and say 'shh', your running everywhere, come and have a nice cuddle with me and a calm down for a minute. He does love reading, so this is a good way I've found to just get some bodily contact and slow down a bit. I don't normally look after him during the week due to work though, and so its not as easy for someone else to do this with him.
I also recently went to a talk by one of the leading experts in dyslexia and in Oxford, England. His name is John Stein (you can google him). He suggests making sure that all of our young ones get enough DHA (Omega-3 fish oil). He says that it helps the brain in its formation, and can reverse or prevent severe learning disabilities. Its basically really good for any brain and can help us as well! I'm not sure if its helped or the behavioral things we've tried have made the difference as we did everything sort of all at once, but gradually over time its all really getting better and our son is finally sleeping more and longer times at once - getting up less in the night is making SUCH a difference to us all.
The main thing is to do some research, trust your instincts that things aren't quite as they should be, and try to notice anything you possibly can about what helps or what makes it worse - both in you, in his environment and in his food. It may not all be immediate, as things like this can take a long time to develop and a long time to resolve. Good luck, you are doing the right thing by reaching out for some help. You will find something that helps you in your own way eventually!