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?

I don't remember PT as being "optional". We had to be there, drunk or sober, good night's sleep or just getting off 4 hours of firewatch. Maybe the Army is different from the Corps?

The way it was explained to me when I pulled the same stunt. If you choose to go out and hoot with the owls, don't complain when you have to get up and scream with the eagles.

Really? You are in the military, correct? you volunteered? you may not want to sound like you're whining but you do! God forbid you ever have to stand combat watches for 12 hours and still accomplish work. You have other hours in the day to sleep. you need to learn to adjust to what the schedule demands.

I recommend you refrain from throwing up----Just do PT with the rest of the company---You're in the United States Army---Not the Salvation Army----What in hell are you going to do in a combat zone???

Having worked in both FORSCOM (USASOC) and in the MEDAC I will say being a leader you have to be more creative to accomplish the mission and keep your Soldiers in mind a bit more in a hospital. Especially with COVID and my staff being worked to the bone we had to find new ways to maintain our physical fitness and still meet the mission.
I would suggest to your leadership an alternative time for PT which is what we did in our section, and our APFT average was over 270, with several soldiers getting their EFMB, Air Assault, and GAFB.
Hopefully with some reason and possibly a good censure of the Troops it can get rectified. I’d suggest talking with your first line or proposing a plan to your chain of command how off shift soldiers will maintain their readiness.

Just go PT and bitch about it later you’re in the military 24 hours a day

Go to PT, really it is at mosts hour to an hour and a half add in the benefit to your health. Look towards the positive.

Army

4-5 hours is good enough without hinder performance and thinking. Thou, 6-8 is preferable. If your lack of sleep due to duty requirement, your NCO should give you permission to do PT in the afternoon and having you report for duty at work-call formation. That is if he betting that the PL and PSgt not going to have his bacon in the morning. Usually, your NCO should have called and arranged this that night. Usually, if your PT score is high, you would not be doing PT that day. However, if you are average or lower, you will be doing PT with your favorite Buck Serge. That's what I have had done while I was still in active duty.

On the other hand, if you were out late having fun, you'll have to suck it up and pay for it. Heck, me and my whole squad came back from our outing, changed, and went to first-call formation for PT and work all day. But when it comes to lunch, we slept like a baby. In Korea, after the Super Bow party, the whole company, 1st Sgt included, were all sh** face during first-call and has to endure the rest of the day.

Getting used to minimal sleep is what you must learnt how to live with, during the invasion toward Baghdad most Soldiers and myself included went for 3 days straight with only 4-5 of sleep, average about an hour a day. I call it, "race to Baghdad". Build character, man, it's building character.

I have been out of the military for 22 years, and in 15 years prior to that. What the hell happened to our military? Sleep deprivation was one thing we could count on back then.