She might not calmed down by 5 if there are no boundaries. I have a friend where it escalated, their daughter went from kicking and hitting them to hitting herself. There was a different reason there, they spoiled her to the max, her wish was heir command and when they tried to put some breaks, she escalated to get what she wanted. As far as I know there is no violence between parents. They are going to a therapist now.
my DD went through a phase like this around 3 years old. Some boys hit her and while she is not brave enough to do that to kids, she took the behaviour home. She started kicking and hitting when she got upset.
it stopped maybe after a month or so. We were very firm, kept telling her: “no hitting” while holding her legs or hands down. That worked partially, the second part was to add consequences: no more park today, no ice cream this weekend etc.
eventually she started saying “I won’t do it anymore”, while doing it the next time. I told her you have to learn, she promised to learn. We went through that 5-10 times, every time she’d promise to learn.
And one day all was forgotten, just like that, she went to be her old self.
we also moved her to a different nursery, that was planned regardless, bc the nursery was bought by a bigger one and everything went to sh-t after it (staff left, not enough supervision, poor meals etc)
she still gets stroppy sometimes, obviously, but there is no more hitting or kicking.
ah we did timeout as well. Staying on a step, until she calmed down and said sorry.
I also praise her a lot, but I always do that. And tell her how proud I am when she does something nice etc.
hope it gets better soon for you too