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?

This entire thread is kind of surprising to me. You are in the Army. You were ordered to be somewhere. You make it work. I worked 12 hour guard shifts, with Guard Mount 2 hours prior, and weapons draw an hour before that. That's 15 hours of my day. Plus, I still had to do PT. We worked 5 days a week. Plus, Our command liked to pull regular (at least once a month) 100% recall formations. Did we bellyache? Yup. Did we still show up? Yup. We slept when we could, and saw our families almost never. It sucked, but it's sometimes just the way it is. When your contract is up, remember this when they offer you that juicy reenlistment bonus....

For some reason I can't here u.

You’re whining. Suck it up or find another career field.

When it comes to "no show" to PT, the 1SG's reaction will always be right in my book, and regardless how radical and extreme his or her "reaction" may look like, (in reference to "no show" to PT). I will always support a legal, proper, and correct orders from any 1SG (male or female).
How do you bring this issue up and solve this effectively and professionally?
First of all, your case is not an issue.
Second of all, your 1SG put out that everyone must show up to PT at either the 0530 formation or the 1600 formation. Problem solve! You know, it takes a bad apple to spoil the bunch.
Make sure through your platoon Sergeant that your 1SG is aware that you scheduled your PT at 16:00. Oops! My Bad. You worked over night. Either way, you must do PT.
Third of all, you confused me a little by saying that your 1SG says that you have to be at the morning formation, and no exceptions.
He (your 1SG) must know something about you, if your statement is true (no offense).
As a former infantry Soldier stationed at Fort Hood with the 4ID, 2nd Brigade back in 2001-2004, four (4) to four and half (4 1/2) hours are enough sleep to show up for PT after an eight hours shift. In fact, I had to show up for PT formation after pulling 22- 24 hours CQ at the Brigade HQ, if not on PT details. Well, we would not win any battle if we cannot adjust. There was a time in Iraq, we had to pull tower duty on 4 hours on, 2 hours off continuously for about 2 weeks due to shortage in manpower. In Kuwait while getting ready to invade Iraq back in 2003, we took great care of our Bradleys all day in a hot sun in the desert until real late. Without any notice, (less than 2 hours) the 1SG just "voluntold" you to KQ, (10 hours shift) and then back to maintenance. We wish we could get rested for 4 hours. If this is a problem for you, you still have an option to not reenlist. As you may already knew, Army career is hard work , and it is not for every body.

Go to pt!!!!!! Pt is to keep you in shape to survive on the battle field it is not a punishment. Being tired will not get you out of the fight in combat your enemy will not hold the fight because you are tired!!! It is a great chance for you to discover your limitations and get stronger!!!! You're in the army not working at IBM.

Your leadership knows your problem and is probably trying to figure out a way to look out for you. They might have their hands tied on the matter though so give them some time to work it out on their end. In the mean time start trying to figure out a good sleep schedule just in case they cant figure something out.

You don’t. You go to PT at one of those times and go back to bed afterwards if you need more sleep.

You can also do PT while at the hospital, you just need to talk to you PSG and PL to have it scheduled on the training calendar.

Stop Whining and start going to PT, if you are only getting 4-5 hours of sleep that is on you. PT is required of all Soldiers - Officers and Enlisted... it also the only dedicated 1.5 hrs of each day that is required to be scheduled on your weekly training Calendar.

If the Commander says PT at 0530 or 1660, you go, period! Sounds like you have a great MOS as far as duty hours are, but you will follows orders or face the consequences.