D&D PvP: How to balance one powerful vs two weaker players.

I'm wondering what levels you think would work best for pvp in a dungeon or other unique environment (possibly multiple rooms and props) if it's one more powerful player vs a team of two weaker players.

Would a level 5 with an uncommon magic item of choice vs two level 3 players be an even match? I figured without the item level 3s multiple turns and potential synergy would be a more likely win, so I buffed up 5s raw power with an item but felt level 6 with no item would be too powerful because of D&D scaling.

What that work, and what other levels could work for this? I want this to be as even of a match as possible.

It's been said many times before but D&D really is not built for good PVP and trying to balance it is extremely difficult.  Just stating "one level 5 vs two level 3s" is impossible for any of us to determine, since it doesn't say anything about what the characters can actually do, their ACs and HP, or any other information that would influence the outcome of the fight.

The two things most DMs go out their way to avoid is players at different levels and PvP so the obvious question becomes how did you even end up in a situation of two level 3 trying to fight a level 5? 

Level 5 characters are absolute beasts compared to lower levels, the jump couldn’t be more noticable. Not only do Martials get multi attack which doubles their output to beat two level 3 characters, but spellcasters have way more options to just stop the other low level PCs from even mattering.

I'm wondering what series of mistakes led to this situation in the first place. Fundamentally you can't balance PvP in this situation. As the others have mentioned, D&D isn't designed for PvP. It doesn't have the kind of rock-paper-scissors advantage negation design baked in and that's a feature, not a bug. D&D is designed as a collaborative storytelling adventure game. If your players are engaged in combat against each other something has gone terribly wrong.

The only way to balance PvP in D&D is to go the IROC route by removing all the variables and assigning all competitors the same loadout. In D&D that would mean everyone plays Xerox copies of the same player character: same species, class, subclass, equipment, feats, spell list, stats, etc. And it would mean even numbers in 1v1, 2v2, 3v3, etc., or an all-out free-for all with no teaming up allowed. A 1v2 scenario wouldn't even work under these restrictions.

So I guess the advice is either accept that there is no way to balance what you're looking to do or... just don't do it?

What is the situation here?

Is this a narrative match like the "Recruit the villain" or " we got the wrong guy" tropes?

Is this PvP because the players couldn't work together?

Is this a case of a villain is given a player to make it more interesting? 

All these situations have different solutions.

Like others said, you can’t balance it. PCs are glass cannons. In D&D, PvP really comes down to initiative/action economy, owing to its turn-based system. I win initiative, and I get my nova attack off before you do. I probably win. If I don’t, and I’m still standing after your nova attack, then I get to go again before you do. 
And stealing the other side’s action economy is what will really win the fight. If the level 5 is a wizard, throw out a hypnotic pattern, move to a safe distance, and leisurely take out one target, then the other. If one of the level 3’s is a cleric, cast hold person on the level 5, and the fight is over.

The whole thing will not be as satisfying as you might think. 

Assuming everyone is on board for this and (hopefully) it's just a fun little deviation from the actual story... you're going to have to "white room" it yourself multiple times. You cannot balance it by loadout alone, as there is already so much imbalance and too many variables even before individual player decisions come into play. In your example, how are you going to know whether the item you (or they) chose is actually going to benefit? I'm with everyone else here: why subject you and your players to this, as it's clearly not designed for such a thing.

I will say that I have seen DnD PvP done, and it was somewhat entertaining, but that was with an incredibly experienced DM, environmental factors that were just as powerful (if not more powerful) than the PCs were to even the playing field, and a group of players who were just doing it for the lolz. Even then, I don't think that many people who watched were all that surprised that the sorcerer won in the end.

D&D PvP is extremely random, particularly for small numbers at low levels. There is a significant chance of a level 5 vs two level 3s ending in one round, with either side potentially victorious. On average I think the level 5 would have the edge, but it's fairly close and depends a lot on die rolls and the specific classes involved.