If this is your first horse, you really shouldn't be getting a stallion. Money factor aside, I'm not sure how many places would even let you board a stallion. Most I know of won't allow them.
If I were you, I would just wait.
Just out of curiosity, why a mini? It's not like they're any easier to take care than a horse that's big enough for you to ride.
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no one is arguing that horses are worthless, people are simply saying that at twelve years of age (and that counts going on 13) it would be extremely hard to earn the money that you would need to take care of it.
i think you should really consider volunteering at the stables. you can be up close and personal with horses, learn some valuable work experience and perhaps your parents can give you the space to learn. it's worth a shot -- and definitely more viable than finagling a way to purchase a horse.

Consider the following once you got the horse
While sure you'll still have extra money since the horse isn't worth 5k, it is still isn't practical to buy one. Oh yeah if the horse isn't going to be bought there in your area, there are taxes and traveling cost to consider.
P.S. Try first learning how to take care of the horses before you buy one. It is better to know it first hand on how to take care of the animal than just figuring it out once you got it.
I'm just curious how if you're not sure how to make the 5k to buy the horse with no job, how you're going to afford the stabling, feed, upkeep, vet bills, equipment and grooming supplies once you have the horse?
I mean there are a few ways to make money independantly like bottle drives, or a lemonade stand, but if you can't do anything away from your parents like pet/house sitting, and don't have a job how are you going to afford the horse in the long run?
Don't get me wrong I'm horse crazy and would love to have a horse of my own, but I can't afford to buy and keep one, and that's with a steady job :(
And the one you're looking at it is gorgeous, but why not try like many people here have already suggested and spend some time around the stables with many different horses until you can comfortably afford one of your own?
sorry to say but you really shouldnt be geting an animal like that... start with something smaller and less money to keep, like a hamster. if thats not big enoth then thenn move upo to cat or dog. whatever. if you get a pony you will only most likely just have to sell it or give it away and all that work you did to get the money for it would be all out the door... gone... it`s hard to keep big animals, so go small first.