I too have a 5 year old son new to Kindergarten and on the second day of school he told me the teacher put him in time out already for yelling and talking in class. Although I know this is a huge adjustment for him, I needed to make him understand that this is not pre-school anymore and I took his video game away from him for the rest of the day.
Even though I am home for him after school, he has a very strict routine when he gets off of the bus. He has half day Kindergarten, so when he gets home he eats his lunch while I look through his schoolbag. After lunch is done, he is to do his homework. I tell him he now is old enough to do what is expected of him. If not, his favorite things get put in the cabinet for the day. There are some days that the cabinet is full of stuff, but now he is learning.
Tell the Nanny to get a routine going and try to stick to it. Boys need structure. I have a very hyper son and it has worked for me.
Hello. Kindergarten is a very big adjustment to little guys and girls. I'm assuming he is in kindergarten and not preschool at this point. There are many expectations on kids these days and lots of kids have a hard time transitioning. He most likely IS tired when he gets home whether hungry or not.
How are things going at school? If they are going well, he may be just holding himself together until he gets home and then letting loose. He can't hurt his sister (or anyone), so I would think maybe coming up with a plan for his nanny to follow until you get home. Time outs can work if followed consistently. Your nanny must remain very calm and have him sit out for a few minutes (up to 5 which feel like an eternity to 5 year olds). I think lots of noticing how well he is doing in school and treating him extra special by the nanny when he gets home would be helpful. In his eyes, his sister may get all the attention. Same for you. Bestow praise and cheers for all things he's accomplished. Have him earn things he likes to do (ie: watch tv.) Get some books at the library about emotions written for kids and then come up with some things he can do (with him) as alternatives to the hitting, screaming, pushing, etc. He can use his words, he can ask for help, he can count to 10, open and close his fists tightly, take deep breaths, go to a special cool off spot, etc. There is a book called "hands are not for hitting" which is good too. I don't know if this helps----- but many many families are going through this right now as their kids are adjusting to new classrooms and routines. Good luck.