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?

Seems to me that there would be a lot of other people in your overall command that don’t have “shifts” ending at or before 1600. If you are the only person on your shift affected by this, the hospital (like all other units being affected) can do without you for an hour - OR - your boss at the hospital can request an exemption.
I also have to ask - is PT being required every single day or is it only 2 or 3 times per week? You don’t mention that, nor do you mention requesting a formal waiver/exemption.
Finally, I got by on about 4 hours of sleep almost every day for 13 months in Vietnam. Most of that sleep was in one to two hour increments since I also had to take my turn on watch every night. Very often, this might be after being out on an operation, or sweep, or patrol or God knows whatever else during daylight hours.
The military is NOT a 9 to 5 job and you had to know that when you enlisted.
So either get an exemption, or arrange to show up late on PT days, or just stop whining.

Suck it up buttercup … there were times we just got into the barracks with enough time to suit up in PT gear and go do what was scheduled
Guys would be puking on the run but guess what, we all made it
You go out at night for whatever reason KNOWING you have PT in morning THATS on you …SUCK IT UP !!

Came in on this 2 years too late, but that's RP: putting old posts front and center.

0700-1500 = 8 hours of uninterrupted sleep. Terrible shift though, nothings open when you come off.

Surprised your section doesn't hold its own formations and PT. That could be a solution.

You’re working against the system because medics are usually the most unfit in a lot of units due to your schedules. However, I do disagree with you reporting after a long shift like that. You can work night shifts for a while but it takes a toll on your system. I lost years off my life staying up for 24/30 hour shifts with a small 15/20 minute nap. You need sleep for your body to recover and sleeping during the day take away from your personal responsibilities. Appointments, running errands, grocery shopping, or whatever.

With today’s technology there’s absolutely no reason why you should have to report after working that shift.

My recommendation is this, buy a good fitness watch, create a PT schedule that is focused around the ACFT or whatever your unit uses to test for fitness. Log your workouts in your fitness app and send screenshots of your workouts with weekly weigh-ins. To take another step is to have more medics from your schedule meet up and do PT together.

I know that a lot of commands are old fashioned with doing PT between 0630 to 0800. But any GOOD leader will understand and work with his people for them to maintain a healthy lifestyle and good motivation/morale.

I hope this helps. RLTW!

Oh poor baby. You are in the military. You sleep when you have time.

Had a similar situation. My company got a new 1SG and he was not aware that he had soldiers at the Regiment HQ that worked some strange hours. Subsequently I was called out of ranks by an NCO whom I didn’t work for. I was directed to Tops office and he instructed to sweep and mop the day room. Of course I did as instructed, The 1SG asked me why I wasn’t in formation? I told him that I was Special Duty and in the past three years have never been in a Company formation. He laughed and said why I didn’t tell him that before he had me clean? I laughed and said “You didn’t ask me, Top. After that he poured me a cup of coffee and we had a good conversation about what my job was. Excellent First Sergeant! What I’m getting at is your Company leadership may not know your schedule and you first line in more concerned about himself than you.

I remember being told, if you want to be out all night partying, that’s fine. However you better be to work in the morning and on time. I never forgot those words. I’m 69 now and all the years I worked I was never late.

So nap from 00:30 to 04:30. Go to PT and go back and sleep after morning meal. It’s called military life. We’ve all done the same at some points in our duty.

Let me inject more to this... your MOS says laboratory specialist. You're far from the tending physician on duty. Way far. Yet, you snivel that you're being forced to PT on minimum hours. Why? Why aren't you using your CoC about this issue? You're airing business that does not need to be aired, especially on a public platform! To hell with your entitlement and your complaint! You deserve some extra duty at minimum for doing what you did, throwing your CoC under the bus. Totally unsat!
Do you realize that big city fire departments work a 24hr shift? There's at least 3 medics riding the buggy in my city, times that by however are on duty. They work a 24hr shift with very little to no sleep and they have to be spot on for their duty hours. You, have nowhere the responsibility that they have and you can't figure out a sleep schedule and you only work a third of what they do? Maybe you should stop and think about shit like that before you open your mouth and embarrass yourself any further. I think PFC Davis is in order here, SPC Davis.
To those who haven't a clue about civilian duty hours, get a clue. The tending physician, the resident, the surgeons who just left and are now back in the OR 2 hours later, e.t.c
I live it, I see it. I also see those same folks at the gym in the hospital before and/ or after surgery work. There's no excuse that she can make to justify her sniveling.
That is all

This post is two years old. I don't know why RP is showing it to me. You probably are not even in the military any more.
From a policy standpoint, you have no leg to stand on. Be where you are told to be, when you are told to be there and quit complaining. The military is only required to let you have TWO hours of sleep. I can't tell you the number of times I got that news when I was in the Infantry. It sucks, and there were times when I had to work with even less sleep than that. You don't need sleep to do PT, sleep after PT.