Cool, maybe you can take over.
It's your turn. You have a shortsword left, and you have the precision strike, menacing attack and pushing attack manouvers. You're at +7 to hit with your Shortsword, and the Monk (AC 19) is standing adjacent to you. You're all full HP with action surge and all Sup dice left, and you're 5th level.
AC of 19 implies the Monk has a +5 and a +4 to DEX and WIS, basically impossible at level 5. Also nobody use Precision Strike but let's forget that. Also, a Fighter could have a Rapier instead of a short sword and would be dumb not to, but we'll give you the benefit of the doubt on that.
Let's start with a standard array (15, 14, 13, 12, 10, 8) and a standard human. The Fighter picked Sharpshooter at level 4 and the Monk DEX.
Fighter has a DEX of 16 and spent loot to buy a Scale Mail (not that unrealistic at level 5) so he has 16 AC. Fighter has 15 CON, thus 44 HP. Let's assume Archery Fighting style
Monk has 18 DEX and 15 WIS, resulting in an AC of 16 as well. Monk has 14 CON thus 38 HP.
Any hits the Fighter inflict will inflict 1d6+3+1d8 (because you can choose to spend your superiority dice AFTER the hit) for an average of 11 per hit (12 with a Rapier), that means the Fighter needs 4 attacks to hit to finish off the Monk. The Monk could, of course, spend the next two turn doing flurry of blows, with each hit doing 1d6+4, averaging at 7.5 per hit, meaning they need 7 hits to finish off the Fight since they can use their Second Wind after tanking four hits to add an extra 10,5 to their HP. Of course, it's possible the Fighter has a second weapon he could draw on their second turn to add an extra attack there.
The Monk is more likely to hit, but the Fighter is more likely to tank hits. It's not an IDEAL situation, but it's hardly hopeless for the Fighter either, especially if they got backup. The Fighter goes first so they'll do 6 attacks before the Monk can let loose their second turn of attacks, so it comes down to the dice roll. The Monk COULD spend a ki to dodge, that's true, but that means they only get two attacks on that first turn and not four and it bogs things down. It certainly keeps the Fighter of his ally so I guess that's not bad in itself.