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?

Army Regulations say you need only 4 collective hours of sleep in a 24-hour day. May want to keep that in mind. I would suggest an ETS if you find that too much for you.

Let me ask a counter-question here. How many hours of sleep do you think you'll get downrange?

My knee jerk response was almost "suck it up Buttercup, this is the Army". Now, after being retired and owning my own company with 65 employees who perform demanding and sometimes dangerous tasks... I think leadership has to look at what they are asking and decide if it is truly in the best interest of the Army, the soldiers, and in this case... any patients who may be treated by this individual. This isn't a war zone scenario where everyone does what ever needs to be done to accomplish the mission, safety be damned. This is a garrison scenario. If it were a short term situation... yes, grind it out and get the job done.
In this case, for these soldiers that work thru the afternoon PT so their only option is the morning PT after 5hrs of sleep after pulling a stressful 8 hr evening shift 5 or 6 days a week, some consideration and better planning should be the course for their leadership. Sleep deprivation may be expected during wartime or even training... regular day to day garrison activity tho? There is no point to it. The leaders are affecting the health of the soldier and potentially creating performance related problems and risks at the medical facility. what's the worst that can happen? Maybe giving a patient the wrong prescription, marking the wrong person's chart to remove a gall bladder or a hundred other life threatening mistakes?
This is also a recruitment and retention issue. Considering the Army's current struggles with meeting these goals, poor leadership is certainly a major reason to lose a good soldier.
Leaders need to perform risk analysis and weigh all considerations, even when simply scheduling a PT formation.

You suck it up, Im a Nam Marine, many times had no sleep.

Yeah the regulation is take your ass to formation !!

Suck it up buttercup!

The new nly way to solve this problem is to do as you are ordered. As a Junior Enlisted whatever that is, you have been granted en an order and you do it. No questions
I hate to go back to Vietnam duty, but I guess you need to know. As an Infantryman, we often did 16 and 20 hour days then started again the next day. That’s what we did. Why did you join the Army?

I don’t understand your dilemma, go to PT.

Adulting is hard, we all figured it out, you can to. Sleep after PT.

Pussy.

5 hours? You're lucky. Quit whining. You're in the military! If you want easy, go work at the Gap