Love the picture! Were you riding independently at 4 without an instructor by your side/holding a lead? Do you think a 5yo with average strength and balance can learn to ride safely?
I grew up much the same as Beau. Very horsey father (professional trainer) and non-horsey mother. She CAN ride, but given the choice, she'd rather stay home.
I was plodding around on my own at 3 and I was working cattle at 5. Of course, the fastest I ever got even then was a plodding lope.
I learned much during that time because I WANTED to learn. I craved it like a junkie and my Dad was more than happy to provide my "fix" LOL. I would pitch a royal fit if my Dad ever left the house with a horse or a trailer and I wasn't with him.
My brother was competing in team ropings by the time he was 6 and he and Dad were often in the money. Not because they were fast, but because they usually made good catches where other teams missed.
I'm a firm believer that the earlier you start to teach a child, the faster they learn and the easier it is for them to learn because they aren't nagged by doubts and random fears like adult beginners or even older children can be.
The most important thing is that they are being taught age and ability appropriate things and are put on a good horse that is both well trained and forgiving of mistakes, which it sounds like your daughter was.
So IMHO, if you want, give her lessons as often as you are able to afford it. One way to help her learn the value of things is to have her "earn" the lessons by doing housework or being helpful in some other way.
I'll also be honest, I was halfway expecting to open this thread and find a person in your situation that was wondering about buying
a horse for their child and IMHO, that's very seldom a good idea LOL.