Hey S.,
Whatever you do don't let the school system label your child with anything. A close friend of mine is going this very issue. Once ADHD gets on the file its on there forever. It sounds like to me that he doesn't have a behavior issue at all. Perhaps he is just being a 5 year old boy, who is a little extra busy.
He could be extremely bored, and needs extra attention or extra things to do. I have boys like that in my Sunday school class. I have sons like that. He could be extremely intelligent, but instead because he has a harder time sitting down the school wants to label him. You know your son better than any teacher. You are your son's first and most important teacher.
Five year olds don't like to sit for long periods of time, especially boys. You sound like a great mom who is concerned about and loves her son. If you have a relationship with the Lord, then my biggest suggestion to you is that you lift this up in prayer. There are still caring worthwhile teachers out there, but no one loves your son as much as you.
Sadly, there are many teachers today just want whatever makes their job easiest. I have friends who are teachers, so I know great ones are out there, but do beware. Also if you test him, please do it privately. There are others schools out there like Montesorri that might be a better fit for your son. There are public Montesorri's out there if cost is an issue. All kids learn differently. Sometimes young children even learn better when they are moving instead of sitting. God Bless you and your son.