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?

If you haven't been on a deployment yet, then this is very minor compared to it.Sleep deprivation isn't fun but your body can handle it. I don't know the regs but in prep for a deployment that means a soldier's ability to withstand a lot of stress, little sleep, and continued physical exercise.
I've done a lot of stuff while in the military that made me feel off and on rare occasions sick to my stomach. As a Medic, we had to have our Aid Bags on us almost all the time or in an ambulance.
Deployments aren't easy. You are a soldier first and are defending this country, those you love, and complete strangers; many of which will spit and insult you b/c they are ignorant. Military standards should return to the higher point they were but that is another topic.

I was Navy. And my answer may not be relevant to your circumstance. But maybe it'll provide a perspective.
Aboard the USS South Carolina as a radio and satellite Communication Electronics Technician I was responsible for the repair and maintenance of a lot of critical systems.
One night I was exhausted. So going to the Chief I asked him if I could get some sleep and fix the radio in the morning.
His standing order for the reminder of my deployment on that Ship, "We're only required to give you ONE hour of sleep per night. Petty Officer Thomas, you may not go to bed until ALL of your Equipment is up."
During the time I was up sometimes 2 and 3 days straight. On a nor-eastern 3 month cruise, I was up all day- all night and all day the next day. Slept 1900-0700 and did it again.
They have the right to ask you to do it. It's a lawful order. I was exhausted many times. But I became a Super Tech. Memorizing block diagrams and schematics. Learning how to use it to get fast results. Then that Chief added another stipulation to my work.
I had to tag each module, if it was a module swap, with every defective component.
Another ET would replace the parts and test it. I HAD to be right in my troubleshooting.
What you take back from being pushed is how much you can do and overcome.

I hate to say it quite so blunt. But I'll tell you like they used to tell us. Suck it up buttercup do your job. We went for days during training with no sleep and still had to do PT. Trust me it really sucks right now but in the interim you will become a stronger and better person for it. Good luck.

embrace the suck and put your big boy pants on and do it what seals go 24 hrs no sleep straight pt the whole time so you cant say a body cant do it on 4-5hrs of sleep

embrace the suck put your big boy pants on and do it

You've got to be kidding me. So you join the military knowing full well the type of "tough love" that is part of the culture and whine about having to PT on very little sleep. all I can say is good luck when you get deployed because you'll get less than that depending on your MOS and theatre you deploy too. Suck it up snowflake....

I get it. I had a similar problem when I worked at the GRSOC. I was intel and did shift work and had basically the same problem you did. We came off 12 hour shifts at 0600, then were told to wait around until 0900 for company PT. That put most of us in our beds around 1100 to sleep until 1630 and get up to do it again.

I was a platoon sergeant at the time so I had a better avenue to the 1SG. I approached her and laid my day to day timeline out (along with my entire platoon on my shift) and made a deal (took a risk) I had 48 in my platoon at the time and about 7 on a weight program. So I said if you'll give me 4 months where I run PT for my platoon on my schedule, I'll get all of them back in regs.

It so happened it worked. Well....mostly. My entire platoon was obviously supportive of the idea and they understood the deal. We got 5 of them off of the PT program and chaptered the other 2 out of the Army. If you've never done a ht/wt separation, you have no idea how many steps there are and how easy it is to get your packet thrown out. I digress....

My point here (because I've been on both sides of this problem) is that your 1SG/CO probably have too many PT failures, too many overwieghts, and an accountability problem. (Medica and MI--we are a lot alike) So they throw the hammer down. So in my opinion, no--it's not sustainable to ask a platoon full of SMs to do PT at what would be the equivalent of the middle of the night. I'm assuming your rotation is every 6 months? If it is a month to month thing then I would tell you to get over it.

Use your COC and openly ask your SL/PSG what you can do to help. Are you part of the problem? Are you overweight? Are you a PT failure of close to it? I've never heard of any command team who is 100% on PT/ Body metric standards who aren't pretty easy to get along with.

I get it. I had a similar problem when I worked at the GRSOC. I was intel and did shift work and had basically the same problem you did. We came off 12 hour shifts at 0600, then were told to wait around until 0900 for company PT. That put most of us in our beds around 1100 to sleep until 1630 and get up to do it again.

I was a platoon sergeant at the time so I had a better avenue to the 1SG. I approached her and laid my day to day timeline out (along with my entire platoon on my shift) and made a deal (took a risk) I had 48 in my platoon at the time and about 7 on a weight program. So I said if you'll give me 4 months where I run PT for my platoon on my schedule, I'll get all of them back in regs.

It so happened it worked. Well....mostly. My entire platoon was obviously supportive of the idea and they understood the deal. We got 5 of them off of the PT program and chaptered the other 2 out of the Army. If you've never done a ht/wt separation, you have no idea how many steps there are and how easy it is to get your packet thrown out. I digress....

My point here (because I've been on both sides of this problem) is that your 1SG/CO probably have too many PT failures, too many overwieghts, and an accountability problem. (Medica and MI--we are a lot alike) So they throw the hammer down. So in my opinion, no--it's not sustainable to ask a platoon full of SMs to do PT at what would be the equivalent of the middle of the night. I'm assuming your rotation is every 6 months? If it is a month to month thing then I would tell you to get over it.

Use your COC and openly ask your SL/PSG what you can do to help. Are you part of the problem? Are you overweight? Are you a PT failure of close to it? I've never heard of any command team who is 100% on PT/ Body metric standards who aren't pretty easy to get along with.

Dadgum millennials!

SPC,
I would talk to your NCOIC to explain the impact your sections work schedule is java having in the Lab Section and work a compromise after having a discussion with the 1SG. That schedule is unreasonable. Either the section does PT on their own (1430) or they are exempt from unit PT or the section changes their work hours - but that is a discussion between NCOIC/1SG/OIC. If I were the 1SG I would take into account the PT scores of the section and the leadership before making a decision.