Flying Firecaster (5e Optimized Character Build)
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This build is able to fly 180 feet in the air, cast Fireball several times and kill probably everything that is visible.
Race and Class
Str: as low as possible, we dont need armor or hit anything within melee range
Dex: You need at least 13 for multiclassing into Monk, i would put at least 14 if not 16 here
Con: Not important
Int: Not important
Wis: You need at least 13 for multiclassing into Monk, keep it at that number
Cha: As high as possible, so try to get an 18
Of course, we are going for Aarakocra, since they have a base flying speed of 50ft. Additionally, we gain a +2 in Dex and +1 in Wis, which are quite useful.
I would start with Sorcerer, the Saving Throw proficiencies are much better, and you get an arcane focus. Then, put two levels in Monk and now you just go up in Sorcerer until lvl 20. The subclass suited the best is the Draconic Bloodline, since you add your Charisma Mod at 6th level in Sorcerer. Take the "Fireball" Spell and also the "Fire Bolt" Cantrip, everything else is really up to you, pick whatevers spells you like. As for Metamagic, take distant spell and the other choice is up to you.
We start with the first two levels in Monk (you can also start with Sorcerer if you prefer the Saving Throws and starting equipment). You gain the ability to Dash as a bonus action, unarmored defense (not that useful since through the Draconic Bloodline we gain an AC of 13+Dex Mod), and the Unarmored Movement.
Now, you are already finished.
At level 6, the ASI should be used to get a +2 to Charisma, so you max that stat out if everything worked out fine.
At level 7, you gain the long wanted Fireball-Spell.
At level 10, the last real thing you should do is get the Elemental Adept Feat, so you really can destroy everything.
So, in conclusion, you can Dash straight up as a bonus action (120ft), now use your movement to fly an additional 60ft up, cast Fireball with Distant Spell and voilà, you're an untouchable Fireball-Shooting flying Monk that can't be stopped. Even if your spellslots run out, you can fly a little bit down (to 150ft), cast Fireball without the distant spell so you can trade your Sorcery Points for spell slots and if even that runs out, just cast Firebolt from 120ft in the air and endless amount of time (maybe think about getting the Spell Sniper Feat, so you don't need to waste all those precious Sorcery Points).
Edit from reader: You cannot move 180ft straight up, since the dash action doesn't add double your movement speed to your movement, it's just doubles your current speed.
Edit from another reader: you can, because you're dashing as a bonus action and using unarmored movement ((50+10)+(50+10)=120) and then using your movement again ((50+10)+(50+10)+(50+10)=180). you dash as a bonus action because you're a monk.