Why is a five-year-old given homework? That seems excessive and unwarrented. At that age almost all children have a short attention span. When I was in kindergarten we sang, danced and painted pictures. It seems to me that children are not ready to settle down until they start first grade. Were your son my child I would make a big to do at the school, or change to another that understood children better.
Hello, I'm assuming by homework---- you are refering to practice of certain things like writing letters. My suggestion is that before doing any sort of table work---- have your son do some physical activity first. I also think expectations for a 5 year old need to remain pretty low in terms of how long they will sit for an activity---- 10 to 15 minutes is about all developmentally they can do of one sitting activity. That is why most kindergarten programs are broken down into such short segments.
As far as hitting, impulse control is problematic for all 5 year olds. In my kids we talk about the stop button. The go button works really well but that stop button is a little sticky and harder to remember to hit. Getting the delay from when a child has the frustration before they actually act on it is important and often will naturally come with time. You may need to start working on it before it naturally happens. Giving him language for when he is upset is important. Read some books together that talk about emotions written with language that kids can relate to. (my son described his bad mood as a storm cloud for awhile . . .) There are also books (one that I love called "hands are not for hitting") that give a simple message that you can;t hit. Talk to him about using his words first. Ask for help (always a biggie), count to 10 and take deep breaths. Sounds silly but if you can get him to stop before he acts (and hits)---- he'll be on the right path. Good luck!!
There is no doctor on this forum. This is the link to that forum.
It does sound like you could use some professional help for your child. Good Luck!
Why does the nanny allow him to hit her? Why do you shout? That is not a good way to control aggression. A quiet voice is better. Is it possible your son is spoiled and striks out when he is thwarted?