What helped in some cases for me:

1. There was a boy bullying our daughter on the playground so she didn't want to go, he was 5 and she 4 or so. One time I went there when his mother also was there and scolded him really loudly infront of everyone. The mom came running and said she will get her husband who does karate or whatever, I just told her to do it but if her son ever talkes to my daughter then I will deal with him if she can't.
2. A girl was biting our son in Kindergarten so he would come home with bite marks, she was half a year smaller than him, he was about 3. We told the principal that we expect them to move this girl to at least a different group so she stops biting him, better that they remove her from that Kindergarten. It went a bit back and forth but then her parents moved her to a different Kindergarden.

If the responsible people are aware, in this case teachers, director and to a certain extend parents, but won't do anything, you did not cause enough discomfort for them to do something.

I'd have another talk with the teacher and director and make it very clear that this issue won't stand. I'd explain to them again why this is urgent and lay out my next steps if this is not solved. Those next steps may involve consulting a lawyer regarding taking legal action, going up the ladder above the director, involving the responsible government organization etc.

Make it clear that if they don't solve this problem they will get another 10 problems to solve very soon. Sometimes people need some extra good reasons to care for a problem that concerns someone else. Make it their problem.

So I used to bully a kid in kindergarten. I don't remember what I was doing at all or the kid even, but I do remember his dad confronting me in front of everyone.

He didn't do anything mean, never raised his voice, all he did was calmly and repeatedly ask me why I was doing it and how it wasn't nice and all that. Just a straight talking to. I never bullied anyone after that.

Kids are scared shitless of adults they don't know, you don't even have to scold them or be mean or anything.

That being said, how the school is handling it is the bigger problem here.

Talk to other parents. There's a non-zero chance that your child is not the only one. Also, for children that young, a lot of the times such behaviour comes from negative home experiences - be it their own parents bullying them, or even just neglect (no corrections, guidance, etc), so you can't always expect help from the kid's parents. However, if you manage to get the involvement of other parent(s) then it becomes more serious, and hopefully will have the staff listen and act.

I'd say principal/director is usually the step after a teacher isn't doing their job.

Can you get guidance counselors, or someone above the teacher involved? Maybe changing classrooms?

It really is the teacher's responsibility to make the classroom a safe place, and if they aren't doing it, escalating the problem is the next step. You shouldn't be scared of school, and if you are, the administration has failed.

Coordinate with other parents. "she goes, or we go"

one time i went to get my daughter from daycare, through the window i saw get getting hit, next to an adult reading a story. i came in, grabbed her stuff, took my sad daughter and never came back. no questions, no nothing, just called them to tell them why she won't be coming back. then changed daycares.

What do you expect the police to do that the director and teachers can't do? Arrest the 5 year old girl?

Does your child tell the teachers or other responsible adults about the bullying in the moment, or are they reporting it to you to then report the behavior after the fact? If your child is not reporting it to teachers when the bullying is happening, it's difficult for them to address it with the girl for it to have a meaningful impact.

This girl will not be the only instance of confrontation your child experiences in life, so teaching them how to deal with it in general so they are prepared to handle it themselves will set them up for success.

You can talk to the principal and ask to have your kid moved to a different class.

Have you tried beating up the bullies father, maybe paying an older child to bully the bully?

Or I guess you could talk to the bullies parent directly. Maybe ask them over to observe the childrens behavior, maybe try and "force" them to be friends?