|There are only four rules: Be a good listener, raise your hand before talking, work quietly, and keep your hands, feet and other objects to yourself.
I'll preface with where I'm coming from. My kids do/will attend ps, and they're talkers and busy. I don't like your son's teacher's approach because of all the reasons listed above - connecting Monday's behaviour to Friday's reward; no way of making up lost ground; the whole punish/reward paradigm. But, it's the reality in your son's, and many, schools.
OP, has your child attended other group classes without you? He may be going through an adjustment period as he learns about being a member of a community and the expectations of behaviour. Public school is, in large part, about conformity.
The four rules seem reasonable, and absolutely necessary for a group of children to learn and get along together. Sure, different teachers will interpret them differently (what is "work quietly"?).
I would approach the teacher with a 'what next' approach. I would ask her how she predicts this next week will unfold. She's not going to change the system, and she's not going to make special accomodations for your child. She is probably already doing things like giving your son extra tasks to burn energy. Your son sounds like many 5 year old boys - busy and excited. It's not likely that he's the first exuberant boy she's worked with. It could be she's doing an indoctrination by fire, that the first week or two will be rough, but then they can get on with the year's learning because more kids will be on board sooner.
Meantime, with your son, I would start talking about perspectives. I would talk about why his teacher has these expectations, and what it means for his classmates when he's not speaking quietly, or he's talking a lot or moving around. I would work with him on strategies he
can control to help him meet the expectations, because the expectations (basically, respect for others) are not going to change for his 13 years of schooling. Your approach with your son can exacerbate or help this situation. Throughout public schooling you may be perpetually bouncing between advocating for your child, and helping your child deal with the reality and finding a way to move forward without the school changing what they're doing.
He could have a fidget in his pocket, something that he can subtly play with to preoccupy his hands and extra energy. You could encourage him to spend the last few minutes of recess on the climber or swing really burning energy, and find out if the school has any way to help encourage him to do this (whoever is on duty might be happy to help with this). You could give him a set time that is just his to be excited with you about all the cool things that day, ie 10minutes at xx time (after pick up) is his to tell you everything exciting, and he's free to bounce, walk, fidget and be loud while he tells you.
The first years of school can be very challenging for boys. Some classrooms and teachers are more accomodating of boys' need to move and express. But even the most accomodating classes have some basic requirements for all students who are not identified as special needs.