To give an honest answer we need more info:
Body height/weight, 400m time, mile time. Were parents athletic? (apple doesn't fall far from the tree) If your name ends in Decker or Rupp then decent chance you can improve quickly.
If way overweight then he can see good progress just by losing weight. We need to know his lesser distance times to see if he has any speed. They can just be time trials..
If your name is Gebrehiwot Bekele, or Manangoi Kiprotich, then 20mpw jogging should do it.
Going 22->16 in less than 1 year is not happening without superior genes, but maybe you have them. If you were completely untrained with the 22 that's a decent sign. If you trained much prior to that, no chance. Since improvement rate will decrease as you get faster, I think you would need to break 20 in 4-6 weeks to be even remotely on track for this goal. And then you'd need to hit 17:30 within 6 months to stay on track. OTOH, 3-5 years of solid training and 16 isn't that farfetched at all. Good luck.
I think you could probably do it. I spent 2 or 3 years thinking I was just really untalented because I was always plateauing at ~21:30, but I got 3 months of legitimately good base training under me and dropped down to 19:55 before doing any real workouts besides the occasional long run.
Now I think I could probably get my time below 18 minutes if I can get a good few months off to focus more on running, so I feel like a lot of people could especially that young. My advice is to focus on building a lot of aerobic fitness before starting real workouts, to the point you should be able to run 5 miles pretty easily a few times a week. At that point you might wanna throw in some harder stuff and add a few races to your schedule and see how much your times drop.
My first race in high school I ran a 3200 in like 13 ish minutes, I think 13:32. Anyway, I'm going to give you some frank advice, I think it's possible by the end of your sophomore year running that 5k, but here is the best piece of advice you'll ever get; stretching and going easy on your easy runs. When you do your track workouts, intervals, tempos, etc, that's when you go hard, but on your easy runs, go easy! If you can, swim as your cross training, get jammers and a good set of goggles, if not, then lift, but be gentle on your back, you'll thank yourself when you're older.