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?

In Vietnam we were lucky to get 3 to 4 hours sleep a night before we had to be up and humping again. 0311 Semper Fi

Suck it up buttercup!

Boo. Hoo.
I worked overnights on the ship, had atleast fire party or a 4 hour watch every night. Last duty muster was 2100, before lights out. Watch from 1200-0400. By the time you got off watch you showered, changed, and planned to be up NLT 0700, to grab breakfast and a cup of coffee for muster…and WORKED THE WHOLE DAY to 1600 liberty call. So, that means 2 hours of sleep in 32-36 hours.
YOU CAN DO IT! You’re young, and coffee is the lifeblood of the military. Once, I worked 3 days straight. Never saw my rack. It was hard, but I survived it, and you will too.

You Follow ORDERS

When I was in initial training, I was rarely on a days shift. My official reville and taps hours were adjusted accordingly and it was rare that I had obligations outside the window. If mandatory PT is part of everyone's schedule, then shift workers should have a different time slot.

When power-hungry senior enlisted "impress" their superiors with great results, but a later incident gets traced back to this, it can ruin a career. Good leaders will stand up for doing the right thing.

Since you work the 1600 hrs shift, there is no other alternative than 0530 hrs. PT tends to be team-oriented and therefore the 1SG or other Sr. NCO in charge of the formations has to probably oversee both PT formations. That's got to be an inconvenience to them as well with their busy daily schedules, and it's all due to only five people showing up for PT. That is what is driving this. Poor attendance demonstrates a lack of mission priorities and discipline by the Soldiers not attending what is a mandatory PT formation for every Soldier or Servicemember in all branches of Service. To have organized PT let's say for example, during the noon hour can affect the flow of the daily mission. So either early AM or late afternoon, and since you work the 1660 shift, I don't know how they can provide you "organized" PT vs solo PT, which misses the point of teamwork in every aspect of your job. You work together as a team, exercise together as a team, and yes, play together (organized sports) or as some go out on the town together in a fashion as a team. The key is together, team, and mission.
Note: would noon work for every Soldier in the command without adversely affecting the mission? If so, then perhaps you could approach them with that option if it works for the majority of the team. Then, you'd have to figure out the dining facility and eating alternatives perhaps.
Question: what "exception" would you be looking for that doesn't exclude PT? Perhaps private PT (Private PT typically is a "given" for every Soldier to do to keep in shape for the organized PT), or perhaps another time slot that doesn't impact the whole team? Have you researched that with the whole Command of enlisted personnel? You are fortunate you have two-time slots, AM and PM. I have never heard of PT other than very early AM so you can get back, shower, and dress for the day's work. I understand your work timeframe is opposite the others at 1600 hrs. How many are on your 1600 hour shift from your command? Can you find a time all these shift workers could perform PT? I would suppose also it would depend on what else is scheduled by regular command daily requirements. Your 1SG and Company Commander have responsibilities that can go far beyond what you imagine and thus impacts their command structure and thus you. The command structure is accountable to the mission. The mission drives all.

Boo hoo do you want some cheese with that wine please show me where you're guaranteed any number of hours of sleep
You're in the United States military for crying out loud

Are your leaders there with you? Remember, you may not be able to be worked hard but you sure can be worked long. I agree, perhaps find a job more suited to your constitution.

Like everyone else, I agree, you are in the Army now. Look up the song. It seemed we were always getting up for PT at all hours. I never had a time when we weren't surprised out of sleep to get up and go from a 5-mile run to an hour of PT. They were preparing us to be able to function at a higher level with little sleep. In case we ended up in Viet Nam.

You suck it up and go to PT. You are a warrior and need to prepare for hard times. The enemy will not wait until you get enough rest.