For a first time horse owner a 5 to 10yo old might be too much for them. You would want to look around 10-15yo. A horse too young will in the end.end up hurting the person. That goes for adult and child. Everyone has this dream of getting this young spirited free horse and most times they do not know how to deal with the problems that come up.
You want to have the horse vet checked and look for any injuries and lamness. This is important as you do not want to be buying someone elses problems and end up spending a whole lot of cash on vet bills.
I would also recommend taking a riding instructor (or someone who is Very horse smart) with you when you go to look at the horse. You once again could be buying a bunch of problems that you are not able to handle.
You need to take lessons.. They cost money. I am a 4-h leader in our local horse club and i would highly recommend getting lessons for a few months and see if this is something you would realy like to get into. I have seen many kids get horses and lose interest.
There are many things to take into account..
Hay,grain, minerals, salt licks,shoeing(Which can be expensive),worming, shots,vet bills,blanets,tack, If you do not have land bording the horse at a stable can be very expensive..
I would recommend taking lessons learn how to muck out a stall and paddock. Learn how to feed them and learn what are important things to be feeding a horse. A horse on just an alfalfa diet might get to plump and founder. You need to know the limits and what will be best for the horse.. Get to know the appy breed. Try getting involved in 4-h or pony club. You need to know what style of riding you would like to do. And please always think saftey first!