@Muse, I don't know if anyone mentioned this or not- but have you considered she just might not be ready for the school environment right now?
There is a world of difference between the ages five and six, and in some kids it can be really pronounced. Whatever learning is actually happening is likely nothing that you couldn't just encourage at home.
But - the real thing happening is socialization (in my opinion), and if she's just not quite ready for it, I actually think taking a break could benefit her.
Also, and you might have covered this already - but I don't think I saw it - please don't get fooled by her intelligence. She is also just a 5 year old.
Why I say this: I was really, really bright and latched onto a few things I loved doing when I was 3,4,5. Everyone related to me like I was a good few years older than I was. This wasn't a problem except for when it was a problem - so, kid-reacting, basically. I would act like a 5 year old, but because I was "smart", I was taught not to do problematic things through a very strange kind of negative reinforcement with no positive alternate provided.
Best I can describe it is, people treated me like I was capable of being reasonable. I don't think a five year old can do that.
I see the same thing in my friend's oldest son - he was a huge baby and he's still huge. Right now he's four, but is the same size as the seven-year-olds. Watching adults who don't know how old he is relate to him is kind of shocking. They think he should have learned all these things already, like the concept of personal space and boundary. He's got no clue. And he's big, so when he makes a mistake, it's big. And then he gets shamed for "not knowing better".
She might be joining in whatever everyone does because she doesn't actually know how to separate from the group yet - it could be the same reason being called out is so frightening to her. In which case, she'd be better off maybe waiting a bit, and doing small-group socialization still (supervised play dates, things like that)
Just a thought.