Well...... just because the other kids seem to be managing it doesn't make the expectations age appropriate. There is a reason boys with birthdays near the entry cut-off are disproportionately diagnosed with ADHD. I am not at all saying yours is or isn't, just that I would never judge the behaviour you describe as inherently problematic in a kid who's only 5.
Maybe take a close look at whether he seems hyper, impulsive, unable to control his behaviour? Is he himself a little baffled by the things he does? Or does he seem unwilling to conform, be compliant, and is (perhaps a bit more intentionally) just looking to liven things up a little? Is this a cry for help in a badly-fitting environment? Or a child who needs help and accommodations with classroom skills? (or both! it can always be both.)
Are there tasks and situations that seem to link to better and worse behaviour? Can you have the teacher try some things for a couple of weeks and see what has effect? For instance, standing to work, being allowed to move around more, a wiggle seat or yoga ball, etc? And from the other direction, more challenging, engaging work?
And make sure that his behaviour isn't causing him to lose recess and activities that allow more moving around/ are more engaging - that's a fast track to a bad spiral in the wrong direction. Teachers tend to come at this backwards, but you don't reward good behaviour by providing appropriate curricula, you GET good behaviour by providing appropriate curricula. And that goes double if there are attention or learning issues involved, and meaningful material is essential to getting the child engaged enough to battle through the extra barriers they face in doing the work.
I know many of you in the US have schools with very different expectations for K, but I'll note - as others of us Northerners have noted in other threads - that our schools would never be expecting a 5 year-old to be writing more than the occasional word.
