I have four children, three of whom are in school. You have to know your child, and it sounds like you have a pretty good handle on him at home.
I think that the problem is, when he is away from you, he knows that he can get away with more. I also know that we would all rather they misbehave at home and be model citizens outside our doors.
I rely a great deal, and put a great deal of stock in a parenting plan called "Love and Logic Parenting". It is not the way that I was raised, and so it is a bit counter-intuitive, and I have to read it often to stay with it myself, but it is fantastic. It teaches your child to reason and think, and you love them through the consequences of their own actions...but you let them deal with those consequences on their own. For example: If it is really cold outside, your five year old will learn to wear a coat. If he goes out with shorts and no coat, and freezes today (or is not allowed to go out on the playground at school--because he did not bring a coat) chances are, next time he will remember his own coat and not have to be told.
The idea is that children will be able to make good decisions when they are older and out of our sight if we have trained them to make good decisions with the small stuff.
If your child is a bully, eventually the other kids will not play with him....his behavior will have consequences that you have no control over, so you might as well not even try and change them. But you can control him. I would absolutely NOT suggest that you change teachers. It is not the teachers fault that he misbehaves. But you are in charge at your house, and I would institute HARSH consequences at home when his behavior chart displays ANY misbehavior at school. I am sure that there is some creative thing to take away from him or something that he hates to do, or hates to be without that will drive him crazy enough to do better at school. With my teenager it was television. Now, we are working on his attitude at home and school and there are rewards for changing his attitude. Time-out just drives one of my sons insane: while time-out is my daughters dream.
You might also, during this already difficult time address his diet. No overly processed foods and no white sugar. And by all means keep a schedule with bedtime and a routine around your home until this difficult time is over. And it will pass. You will feel better and so will he.
hope this helps!
C.