I think it's a bit much for a 5 year old. With 2 jumping days AND a conditioning day, and then I'm not sure if the hill climb is just a hack day or another conditioning day. It's a lot of pounding on a young horse. Ideally I'd only do one jump school a week, one conditioning day, have one day where we'd just do long walk hack, and of course a day or two off. Keeping in mind that I would be incorporating poles and cavalettis into my flat work as well.
Honestly, I don't even work my prelim mare that hard. And I usually only jump once a week, unless I'm doing something special like trailering out for a jump or xc school, then I'll do twice. I'm more a fan of working 3 or 4 days on, 1 day off, instead of 5 or 6 days, as it breaks everything up and the horse gets more recovery time, which I feel is extremely important, especially with a young horse.
Pre-training is not really all that strenuous, I don't think an 8 minute gallop is necessary for pre-training, where you're only going 400 mpm for 4 or 5 minutes. I personally would replace the gallop with some interval training, trot/canter sets are better for conditioning than just galloping around, and lower impact to save the horse's legs. Trotting and cantering up hills is excellent for conditioning as well, you get more cardio workout bang for your buck, without all the pounding of galloping. 1 day of conditioning a week will be more than enough for a horse that is getting worked regularly 4 or 5 times a week imo.