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?

Deal with it or look to another career. Problem solved

Regs leave plenty of room to F over Soldiers. Seek resolution from the chain of command. Just start from the bottom and work your way up until you get resolution. Be sure to present alternate, workable options such as your section doing PT separately.
You can also use your operational chain of command to solicit support. A doc might mention casually to the Company Commander that his PR program is adversely affecting the performance of your section.
If you work this issue in good faith and get no resolution, perhaps you can take comfort in being the 50 millionth US Army Soldier to endure a shitty situation. Our sacrifice of our freedoms for the benefit of others is a huge part of why we get respect from civilians.

Sorry to say but you are whining. Even if you do only get 4 hours of sleep, it should be plenty of rest for PT. My group used to work a 2,2,2 & 80 shift. After our eve shift (1600-2400) we’d , shower, change & go out till the clubs closed. Get breakfast & PT. Yes it was only twice a shift but I was 32 yrs old & did it without fail!

Suck it up buttercup

Are you serious? You’re not serious. Please say you’re just trolling. Get some fortitude. I’m embarrassed just reading this utter whining.

Jesus I was a 1SG of a medical company in combat and they ran the only clinic on the FOB 24 hours a day (12 hour shifts) so I have some basic knowledge and experience. My Soldiers did PT and managed well. The one thing no one is mentioning is he has over 16 hours of off time. Sure after shift it may be hard to sleep (too worked up to sleep) so do PT it'll help relieve stress and I promise you will sleep well after. I'm 49 now retired I can hardly sleep past 0500 and I go all day but trust if I can get 30 minutes sleep now and then I do it. I wanna call out SOFT ASS ARMY but I have kids in their 20s so I get it and like I tell them you chose your job when the time comes and you wanna change it, it's your choice. Until then suck it up buttercup and get it when you can!

The 1SG noticed? Shoot if only five Soldiers showed up to PT I wouldn't just notice I'd be furious. I was a 1SG in two totally different companies. Last time I checked an APFT is mandatory and you must pass (if not eventual chapter 13) to be promoted etc. So the next thing you'll say is I do PT on my own, ok does everybody so PT on their own, and do they all pass? The 1SG job among a million is to ensure their Soldiers are trained which includes passing the APFT. And 4 or 5 hours of sleep are you kidding me? There was times I didn't sleep all because of mission. So without out sounding like you're winning, you can forget. The enemy don't care how much sleep you did or did not get SOLDIER UP! And you have plenty plenty plenty of time to sleep maybe between 0000 to 0500 isn't enough (for most it is) but what the heck are you doing after PT until 1600....yeah WHINNING!

You solve that by going to PT.

Are you fucking serious?
What a whiny li'l bitch you are. If you get away with this, then what's next? "I was up late watching a movie"... blah, blah, blah.
You've got the whole rest of the day, take a nap before your 16:00 shift and grow a pair.

I have only one word WAAAAAH!