I recently attained my Promotion status and was made Squad Leader and have a SGT/E5 as a subordinate. How should I manage that situation?

You received your P status, so I take it you know a thing or two about leadership. Lead from the position you've been set to. Whether you have an E-1 or E-5, your position as their squad leader is the same. That being said understand that the E-5 has earned their stripes, and can perhaps be very beneficial to the squad, but not as the squad leader...because that's you. Leadership isn't about rank. Just remember that. I've seen PVTs with better leadership skills than some 1SGs..
This is a great opportunity for you.

Having been a team leader and a On Scene Leader I have had few opportunities to be in a similar situation. Be mindful of how you put things, also don’t be afraid to lean on them some of them for some support for their experience but you still have to be the one that leads. A good leader understands the strengths and weaknesses of his team and knows how to use those to the team’s benefit.

Best words of advice I got after I messed up during a drill “you gotta remember your still learning too”.

You gonna mess up and make mistakes own then, learn from them.

First you must recognize that there is a difference in authority by rank and authority by position. Authority by position always trumps rank, that is why a SPC/E4 MP can dictate orders for the purpose of law enforcement to a COL. Don't confuse the two, though. When dealing with operations of the unit, you have control over the E5, but in matters of general military authority, the E5 has power over you. In other words look at the dynamic of a 1SG/E7, who has operational authority over MSGs/E8 and SGMs/E9 in his/her Company. When it comes to running the Company, the 1SG has the authority over those who outrank him/her; likewise when in regards to running the squad, you have the authority over any "subordinate" who outranks you as well.

Be the pace-setter. Make him keep up. There will be friction.

Like an NCO in an E6 slot you hold.

Sorry - NCO business here! I would have tore up that one... For some of you young Officers, do you write your Battalion Commander’s or XO’s? Think about that one for a minute... Done thinking - Where is his authority for UCMJ? I would let s/he open with what they would like to do, upon hearing them out, would offer some mentorship and nothing more! Sorry Gents - some poor guidance, guidance with no understanding, no real experience with the matter!
This is not anything more than the common practices of accountability purposes.
Or, you simply have a fast burner and a 1SG does not have the faith of his current NCOs, or, quite possibly has underlying circumstances that the young SPC is not yet privy!
All said and done, a subordinate with no UCMJ jurisdiction or authority isn’t writing-up anyone...

I feel for ya. I've seen your situation play out before. It's not normal, but it does happen. It's one thing to be in charge of people who are the same rank as you or you may have been buddies with--been there, done all that--but I don't envy you the situation you are in. You've proven that there can be differences between rank and responsibilities; just treat the SGT as an NCO, being in charge of him doesn't negate the fact he is one, work with this person to get "buy-in" for the situation you find yourselves in. Make sure the rest of the squad understands the situation, but shows correct respect for this person's rank too, and carry on. Hopefully, your chain-of-command will make adjustments in the near future.

You don’t manage it. He is a noncommissioned officer and you are not. I would not worry about this for too long. Your 1SG and CSM will solve this problem for you and address the problem where it belongs, whoever the jack wagon that thought this was a GFI.

It's a difficult situation they put you in. Best of luck. Sorry that I am not able to offer any advice.

Be the squad leader. When in charge take charge. You wanted it so own it.
"Would you, could you and "Hey need you to do this" goes a long way. When soldiers value your leadership it signals trust.
Take care brother!!