I am being told to go to PT by the command on only 4-5 hours of sleep. As a junior enlisted, how do I solve this problem?

You need to suck it up and follow orders. PT is for your benefit, i wish that my current employer paid for me to stay physically fit. If you don't like this answer, you are in the wrong profession.

I'm guessing that I don't have to ask that you've never been in combat. You do your job no matter how many hours that takes, rest when you can, and start again. No time outs, no "do-overs" and absolutely no excuses. My suggestion to you is doing your shift, go to PT, hit the rack & quit whining.
MAJ. L. Koppes U.S. Army (Ret)

When you're in combat you sleep when you can, no matter how many hours you've been up. You do your job. So, my suggestion is to do your shift, go to PT, then hit the rack & quit whining. - Maj L. Koppes U.S. Army ((Ret)

what stops you from going to sleep off PT?

You need to use the chain of command, that's why it's there. Whoever is in charge of your section should be handling this, not you. Now if by chance you are the one in charge of your section, then it's up to you to address this issue (on behalf of the section) with the first sergeant. Don't go to him with a problem unless you also have a solution. On the odd chance that he turns a deaf ear, be prepared to respectfully request to speak to the company commander on behalf of your section. Don't make this about you.

I disagree with most of the comments in here. If you are working 1600-0000, and the first pt session available is 0530, naturally that's only 4.5hrs of sleep. Regulations say that service members require at least 7hrs of sleep. Sleep is a required commodity as is food and water. If 1sg wants pt at only 0530 or 1600, then they should reconsider the shift schedules to align with PT. It is unreasonable to expect a person to have their personal time between 0000 and 0430 when everything is closed dont be stupid. Regulation wise 600-20, tradoc 350-6(pg 52) I know its tradoc, but i think there's a compatible forscom reg.

Not sure how you're not able to make PT. You can do the 0530 PT; take a nap after work and before PT. Then sleep during the day. Like everyone else is saying, work on your time management.
I was in the Navy and I was my divisions PT coordinator. I made PT mandatory. I couldn't risk anyone out of shape or getting heavy. I worked in the engine room on the ships and we had to be able to escape through hatches.
When we were underway I stood the 1800-2400 watch, mustered at 0700 for work, done with workday at 1600, and back on watch at 1800-2400; this could be anywhere from a week underway to months.
Guess what? I still found time to sleep and PT; plus, working out made it where I could function properly on 4-5 hours of sleep daily. I told my boys it didn't matter if we were underway or not, PT was mandatory; most of them had a lot nicer underway schedule than I did. I told them if I could PT on the little time off I had, they sure AF could too.
Not to be a jerk but quit complaining, go to PT, and learn better time management. Like others have said, if you deploy, 4-5 hours of sleep is a luxury.
Welcome to the military kid!

Go to PT?

I'm an old soldier and can't believe I'm actually reading a post like this. Don't want to sound like you're whining? You are!

Fallow instructions, do as you told, report to your first line supervisor and let him or her know of your situation.