When he's misbehaving in school, he gets lectured, punished, grounded
Honestly, remember that he's FIVE, not FIFTEEN. Grounded??? For real?
Think along the lines of this:
Tool: Try reverse rewards
Age: 3 to 8 years
How it works: Take a page from teachers everywhere — kids respond much better to positive reinforcement than to reproach and punishment. And they also like structure and clear expectations. Ruth Peters, the clinical psychologist in Clearwater, Florida, advises parents to take advantage of these qualities by setting up a system of rewards. You can make this system even more effective by reversing the usual rules — instead of giving rewards for good behavior, take them away for bad behavior.
Real-life application: Put a few things your child loves — these could be a Hershey's kiss, a new colored pencil, and a card good for an extra bedtime story — in a jar or box as the day's rewards. Then draw three smiley faces on a piece of paper and tape it to the jar. If your child breaks a rule or otherwise misbehaves, you cross out a smiley face and one treat disappears from the jar. An hour or so before bedtime, you give your child everything that remains.
We did this with a jar of pennies. Each kiddo started each week with a roll of pennies in their jar (because hey, it's only .50, but it LOOKS like a lot of money) and each time they acted up, they had to go get 2 pennies out of the jar and bring them to me. At the end of the week, they got whatever was left in their jar.
The reason it works is that it's clear, concise, and it makes sense to them. PLUS they can SEE the money disappearing and they want to make it STOP disappearing. It's MUCH more effective than giving them X in order to get them to behave.
So, every time junior comes home with a negative report, he has to take a specific number of pennies out of the jar. (or whatever is in it, doesn't matter if it's jellybeans or anything else that has value to him) A good report, you congratulate him, but don't GIVE him anything - all verbal and emotional reward. On the days he has to give you pennies, you discuss the report, accept the pennies, maybe comment about how many are left, and then go on with your life.
Do NOT make a huge ginormous deal about the misbehaving - lavishing NEGATIVE attention on him is going to be no more effective than lavishing positive attention on him. At that age, attention is good - no matter what.
Don't think in terms of punishment - think in terms of logical consequences. And for gawd's sake, you don't LECTURE or GROUND a kid who doesn't have the cognitive abilities to 1) pay attention to a lecture or 2) grasp why they're grounded or even what it means.