I do not like your third point; you should ABSOLUTELY NOT engage in any interaction with the parent(s) of the bully. I've worked special education for years, and there isn't a single child with bullying behavior that isn't himself/herself reacting to stresses you don't see. Simply asking for reparation or apology may cause said child to miss a week of school while the bruises heal. Instead, focus on the school. As you stated elsewhere in your answer, IT IS ABSOLUTELY THE SCHOOL'S RESPONSIBILITY to handle the situation. Teach your child to accept that bullying exists and handle things correctly

(Continuing) "correctly" is a skill to be learned. You should have help with the school guidance and online resources. It is your responsibility, time consumingly frustrating as it is, to convince the school to do what is right (and lawfully required, at least in the USA).

@Dúthomas: thanks. I was out of my depth. Edited.

@Dúthomhas : I have personal experience (as a witness) to back that up. One of the worst bullies at a school, the biggest troublemaker, who couldn't stand still a second and was as undisciplined as one can hardly imagine... I've seen him with his parents at the theater. He behaved like the most perfect angel, a poster child of discipline. Sat straight, didn't move, didn't make a single sound, was polite to the extremes with everyone they met. I'm almost certain that if someone told his parents of a new misbehavior at school, he would have gotten a severe beating. And not changed in the least.

"Tried to find him but couldn't" absolutely WILL NOT DO. - I brought a toy from home once (granted it was daycare, but still), and asked the attendant to mind it for me and specifically stated, so that no one breaks it. Take a wild guess what happened to my first edition Optimus Prime, and what the level of my respect for authority was reset to. That's a memory that's over 30y old and I can still picture the shelf that I pointed to requesting where it should go. IDK, good thing/ bad thing? because I now have NOTHING but respect for the law, the bad thing is that the rest of you can KMA

@Maz: also, try pulling that line when the parents come to pick their child up!

@mazura Our school specifically prevents kids bringing stuff in for that reason.

My favourite example of "no parent to parent" is when a girl bit my daughter in nursery (they were three, it happens, didn't happen again) and the poor nursery nurse had to be very clear to us that they wouldn't say who it was, while my daughter helpfully and insistently reminded her of the aggressor's name.

Keeping your children safe while they're in their care is their absolute top priority, trumping any educational objectives. I believe that is their duty in an absolute legal sense, in loco parentis.

@Dúthomhas The categorical "don't tell the parents" confuses me. It'd be one thing if you said "leave it to the professionals", but you're suggesting that the parents can't be allowed to find out in any way because then they will beat their bully child. This almost sounds like a smear against any parent whose child exhibits a bullying behavior, the majority of whom I expect are not abusive parents. ...

@Dúthomhas ... A much more likely problem is that the parents, who naturally love and support their child, won't believe that the child could do such a thing unless they saw it with their own eyes. They'd be hostile to the person telling them but protective to their child. However, your "bruises" scenario posits that they will believe it. And that means it can only be worse if they hear it from a "professional authority figure", whom they're more likely to believe than a random other parent. ...

@Dúthomhas ... So how can even the school staff ever bring it up with the bully's parents? You're saying they will cause those very same "bruises" if they do. And you don't seem to think that victim parents can ever resort to legal action, even if a misbehaving child causes major property damage, injury, and medical bills. We have to hide a child's naughtiness at all costs based on an assumption that their parents will beat them if they ever hear about it?!

@nanoman The difference is that the school has both a duty of care to the child and a long-term feedback loop they can assess. If they tell the parents, then the child is off school for two weeks and comes in a bit shell-shocked, they'll notice that and it's their job to take the appropriate steps. More importantly, the school may already have information that will alter their decision making on this, that you simply don't. If you do it, there is no obligation on you to monitor the impact on the child in question and you would struggle to do so even if you wanted to.

@deworde Are you suggesting that schools should be considered a required clearinghouse for any interaction between families who don't know each other well, in case a parent somehow gets upset and takes it out on their child? To me it sounds like a bizarre and unnecessary constraint. If a parent is the type to beat their child, who knows what sets them off? It's terrible and we should act when there's evidence of it, but I really doubt it can be effectively reduced by preemptively walking on eggshells with every parent just in case they're abusive. ...

@deworde ... And an incident that should be discussed with a child's parents can happen outside of school, perhaps during a long school break (like summer in the US). You may not even have a child attending the other child's school. And perhaps you will say, "Don't let your child interact with any child you don't know, other than at school" -- but that will be impossible, e.g., the moment they attend a birthday party where the host also invited other little friends from a different circle.

@nanoman Yeah, you might think that, and you'd be partially correct, but not wholly, based on the statements above of someone who literally works in special education. There's just no upside to talking to the parents directly until you're confident the school has failed to do so. What is the OP, who is, lest we forget, a man considering teaching his child to physically assault fellow five-year olds, planning to say that the school can't say far more consistently and with more authority?

@nanoman You may not believe that I understand your POV, but I do. You are still wrong (and grossly misrepresenting my words). You are NOT the ultimate authority at school! And if you confront another parent and make it more difficult for the school to provide a safe learning environment for all their charges, not only will all parties involved not like you, you can be held legally liable for the consequences. The likelihood for a bad outcome for all, including you and your child, is far greater than any good one. Work with the school. Take it to the district if necessary.

@deword I worked in special education. I was no one particularly important in the system (except to my students). Due to COVID-19, alas, I no longer have a job.

@Dúthomhas And I'd like to learn from your POV. Is your emphatic advice limited to bullying that occurs at school? I'm struggling to understand what you would recommend when an incident occurs completely outside a school context, when you have zero connection to the misbehaving child's school, and/or during a long school break. Life is bigger than school, different families have many occasions to interact with each other, so what exactly is the trigger for your rule "keep quiet lest you get the kid beaten"?