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?

SPC(P), Most of the responses you are going to read have been written by folks in traditional field units. Good answers but not relevant to MEDDAC. As a former MEDDAC CSM, I will tell you it's a different world. Let's look at this from the perspective that NCOs are entrusted with the health and welfare of their soldiers. They are also responsible to accomplish the mission. Your physical fitness is part of the mission. However, so is safety. Let's consider what would happen if we required a soldier to operate a vehicle with insufficient rest and they crash it. A 15-6 investigation would look for contributing factors which lack of rest would likely be one of them. So, a soldier who works an 8-hour shift, gets 5 hours of sleep and drives to PT has a car wreck on the way there or back to his or her quarters, the cause of the accident would be just as attributable to lack of rest. Who is responsible? The First Sergeant. In a MEDDAC, the First Sergeant must have a PT schedule for soldiers on every shift. The Command Sergeant Major should ensure the First Sergeant is doing his job, correctly.
You have several options. One is to request to see your NCOIC and then the First Sergeant. If the First Sergeant doesn't fix this, then the next step is the Command Sergeant Major. If those individuals don't understand the importance of safety, you can contact the installation IG and ask them if you are entitled to 8-hours of uninterrupted rest between shifts. You are a SPC(P) so this is a good developmental learning experience for you.

I agree with other about time management on the part of the member posing the question. I would also add: You have identified what you believe to be a "problem" because the PT sessions apparently aren't convenient for "your" life. Then you are expecting others (this forum being a group of others) to come up with a solution including possible regs. How about proposing your own solution, making a proposal, and getting credit for initiative instead of being a whiner. I have a proposal in mind, but giving it away would be robbing you of your own personal growth and journey toward potential leadership. When you reach those positions to be of influence to your subordinates you will have this experience to reflect on and perhaps solutions to delimas similar to this.

You are whining. Get up, or, shower and go back to bed. Nothing compared to the old days.

You go to PT.

Do the people in the morning and then go back to bed, or talk to your shift supervisor about adjusting your schedule.

I don’t see the problem you go to PT can you do the damn best you can. If you don’t pass I don’t do well enough to satisfy the instructor then you have a discussion about why you did so poorly.
Commanders also have to make a choice between two different things how important is it for you to get a good nights rest and how important is it to get this PT thing out-of-the-way. I’m not claiming that all commanders make the right decision I’m just saying that as an enlisted man your job is to be the order unless there’s a serious legal or more reason not to.

You are a United States Military person deal with it. when you are in combat you wont get sleep

Take naps when you can, reduce caffeine intake close to end of shift. Stay away from computer screens, tablets, video games etc close to end of your shift. When you are in bed, your bed if for sleeping; not checking phone, not watching tv. Go to bed after PT. If you have dreams of firefighting or nursing after your career, get used to sleep deprivation. 24 hour shifts with 2 hours sleep if it's a busy shift. Midnight to 515 is more than enough time to get some rest, go to pt and the sleep afterwards. Late shifts suck, but it's doable.

you can get 4 hours sleep, do your pt, then get the rest of your sleep after pt