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?

It seems like your section NCOIC/OIC have no backbones accepting this nonsense. They should approach the 1SG/CO with an alternate plan: PT 1330-1430, Hygiene/Meals 1430-1530, Formation/Duty 1530-1600. It's your Section NCOIC/OIC's duty to recommend this to your 1SG/CO.

How about Option 3 - a mandatory PT session built at a time for this shift. As a military leader, we are to take care of our people...sometimes that means we are the ones who bend. PT, yes, needed. On a rigid time that benefits the 1SG vice the team, not needed. When on home station duty, we need to remember our service members have real lives as well. Many are taking college classes using TA - let's get the mission done while setting them up for success.

nothing will or is going to happen because they will always pull rank, this is an ego trip type bs "look at me and my rank" situation. did he put out the proper information for the initial pt session and if so why didn't anyone brief this first sarnt about how schedules work around the hospital and that different shifts operate on diff times? I do not see how hard it would be for him to has his senior staff come out with a proper way of doing pt and a proper way for the first sarnt to micromanage I meant to come by and check-in or even join the pt session.
Ultimately though(as sure as I am that NCOs ask soldiers to have everything in the company done before anyone could go home and it was after end-of-day formation) they will always "PULL RANK!!!"
GOOD LUCK AND THANK YOU FOR YOUR SERVICE....

Frankly, this one is pretty easy....you go to PT. ANYBODY who has deployed will tell you that 5 hours of sleep is a luxury. Besides, you are assuming that you have to sleep at night. I see a huge window in your schedule from roughly 0700 to 1600 where you can get a solid 8 hours sleep...unless you are not telling us the entire picture. I get that you don't like it, but there are many worse situations I can think of. Shipboard life is typically port and starboard (12 on and 12 off) PLUS a 4-hour watch. Combat patrols are sometimes days long and have VERY FEW opportunities to sleep. The bottom line is that it is a lawful order and you need to follow it. Military life is a life of sleep deprivation - get used to it.

So my schedule is 0630 pt work 900-1630 and then go to bed at 2230-2300 and get less than 6 hours of sleep, waking up to get to pt and still having time to sleep you'll be fine.

Hate to say it this way, but suck it up. Don't know how many times I worked an 8 hour day, had 4 hours off (or less) and then pulled the 20-24 or balls to 4 watch and then worked another 8 hour day. I'm surprised your leadership cadre let it get so bad that only 5 from a whole company showed up for PT. Normally something like that is considered a standing order and you don't get to pick and choose what orders you follow.

PT on 4-5 hours sleep was standard operating procedure when I was in

You are in the Army, aren't you? I know it's not the Marine Corps but you better man up. Just kidding about the remark suggesting the army is less than the Marine Corps. But I was dead serious about you manning up. I can recall so many times in Vietnam when we had contact and most times it wasn't at the perfect time. And I can also recall going without sleep for a prolonged period of time and then having to hump all day up and down mountains during the monsoons etc. My point is that yes, you might have been tired. But that's life my friend. Many times you might be called on to perform with little to no sleep. You don't request mast to resolve the situation. You pick up your gear and get with the program. And bitchin about it won't do anything.

if you get 4 to 5 hours of sleep, what's your complaint? Do you think our enemy will be as cordial?

I could be wrong in this situation, but it looks like a normal situation of a new command. What I saw repeatedly in different units while on active duty is that the new command CO and 1st SGT are not from the field they are now in command of. It seems that any commander from the medical field should know how life support/health care work and should take charge of his NCO and reschedule as needed. I have seen many units that used a sign in roster for pt to be able to show for further inspection that the unit is physically up to par.

I have also seen a lot of officers and higher NCOs that are from other units, or that have reclassed, come in and not understanding how a MP unit, or field hospital, or maintenance unit is NOT SF. This often happens after a life altering injury and reclass out of an infantry unit.

Unfortunately, the only fix I know of is time. Sometimes after reenlistments drop, or enough requests for pcs, the upper command will see it and make a change. If you love your work, stick it out and command will change again, or you will go somewhere else.

Best of luck.