5 year old suddenly gained confidence in school and became disruptive

My 5 year old is a very smart kid, quite advanced for his age (they've barely started to learn letters and numbers in school and I started teaching him to read when he was 3, so I wouldn't be surprised if part of it was boredom).

At home (just focusing on the negatives for now), he's controlling, disruptive, naughty, loves pushing boundaries and doesn't give two shits about consequences. We are trying to deal with it properly at home - we've tried every single gentle parenting technique under the sun and the only thing that has worked with him is a more authoritative style, including spanking. He needs very firm boundaries and immediate, uncomfortable consequences (sending him to his room, removing TV - we don't usually have TV on much anyway - or toys will do absolutely nothing).

At school, he's always been very shy and reserved and well-behaved, overwhelmed by noise and talking etc. This year has been much better - kindergarten has brought him out of his shell, he's developed a wonderful social life and has gained a huge amount of confidence.

The problem is that now, suddenly, he's bringing his bad behaviour to school. For the past week he's not listened to his teacher, he's made other kids laugh on purpose during quiet work/story time, he's shoving his hands in other kids faces (like he does to us) just to provoke them, he's snatching work away from the other kids, all just for fun. He's testing the boundaries all of a sudden, trying to see what he can get away with. We want to nip this in the bud IMMEDIATELY.

We want to do this in three ways. First, to make sure he's getting enough stimulation and positive attention at home, we're doing rough play with him to get his energy spent. We also need to do more quality time with him (but this obviously has its time limits), and I might start doing more writing and maths work with him at home because he's not being stretched enough. Or maybe teach him music.

At the same time, we want to make sure he understands that this is absolutely not acceptable. For one, every day that his teacher tells me he was disruptive, he's not allowed to play with his friends in the school yard after class. Beyond that, I don't know how else to send the message. If I send him to his room he'll just draw for hours and play by himself. I can't really empty the room of toys and activities because we have a tiny apartment and he shares the room with his little sister.

If you think "talking to him" is missing - for one, we always ask him about an incident, but he's not good at expressing himself verbally and we think it's really a 1-dimensional problem. He just wants attention, and to find out where the line is drawn. Furthermore, he HATES being talked to too much. Anything more than 1 sentence and he tunes out.

Please let me know if you have any suggestions.