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?

Listen Sad Sack... If you're writing something like this, you shouldn't even be in the service. Put on your big boy pants and man up.

Go to your first line and request shift PT. The army has multiple MOS’s that require to work shifts. MPs do it, cooks do it Medical personnel do it. MOS’s with shift work should do shift specific PT.

After I work my 8 hour day shift 0315-1300 (sometimes later if someone decides to try and sneak drugs into the gate) and then we do PT right after we get off.

But for Swings for instance we would go into PT at 0930 before a 1200 weapons draw and 1730 before a 1900 weapons draw for Mid shift. It’s not an unusual thing to do shift PT. Easiest thing to do is request that it be that way.

Having worked night shift after my Marine Corps service, I feel your pain. From working against your body's circadian rhythm to daily outside noises, I don't think people who don't work overnight fully understand how hard it is to get quality sleep to begin with, which is what's indirectly being asked of you.
I would raise the issue that this is pretty counterproductive to PT's intent, especially working in a medical environment. Averaging 4-5 hours of sleep with work and PT under the added stress of discipline is asking for a compromised immune system. I'd address this with my chain of command and ask for some sort of exception, even if that meant spending lunch doing my PT instead.

You have 9 hours after PT to sleep. What's the problem?

change your habits !! go to bed early get plenty of sleep. or just pt drunk ! we did it in Germany way back when. most guys ran better on Mon. then on Fri. get your shit in gear.

I was Junior enlisted at one time and you have a couple of options.
1) Talk to your PLT SGT and explain the scheduling issue and request an earlier or later time;
2) Talk to your Supervisor if you are uncomfortable talking with the PSG;
2) or show up,show up at 0530.

Awww you poor thing. You have a swing shift, and no way to make accountability with anyone, and you are whining becuase you have to wake up to show up. Maybe you should go talk to the Behavior specialists in the stress office so you can find some way to manage your time, or GROW A PAIR, get your Team leader, Squad leade, and PSG and march them ll into the 1SG;s office and explain tohem that whle everyone else is given their 8 hours to speep, you re getting fucked becuase you are on swing shift without a solution to accountability.
Here's your solution cucpcake: CALL YOUR PSG for accountability, then go back to sleep, OR maybe your entire shift should go to your shit manager and have that person step up and get their accountability done with 1SG so you all are not affected negatively.

Stories like yours are why soldiers are get out because of a lack of common sense leadership. The army has work/rest cycles that were "supposed" to follow but never do. If you work an odd shift leadership "should" take that into account and tell you to do PT at a reasonable time with your shift supervisior....or do PT on your own. I work a night shift and it never suprises me how leadership at all levels forgets that not everyone works durinng the day only.

Lol get you life together and learn some time management skills...

There is no problem to solve. You're in the military -- go to PT.