Falco? (5e Optimized Character Build)
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So I found out that you can have a character that flies at 160 feet per round and can still do stuff. Let's call himmm... Falco. Also, go to "Detailed Build." For specifics on how to build the fastest Aarakocra in existence. If someone outpaces my build, give the page an edit with a VARIANT version and comment on how much better you are than I am. I plan to use this build someday so please do not actually remove it even if you find a faster flier.
Start with an Aarakocra with blue feathers. The exact appearance of your character is up to you, but we're going to go with blue feathers for no particular reason. Being an Aarakocra gives you 25 feet base walking speed. That's pretty lame. However, it also gives you a flying speed of FIFTY (50) feet! That's the highest base speed in the normal game, and we're just getting started. Keep in mind that you can't be wearing Medium or Heavy armor to use this flight, but we won't be needing it anyway. Make sure your Dexterity score is decent, and Constitution too if you can manage it for reasons of health and safety of course. It's Talons racial trait gives you starting damage of 1D4 slashing damage (Not including bonuses) per hit, and gives you proficiency with unarmed strikes, which will be helpful later. You want to know why?
I'll tell you why! Because you'll be a Monk, of course! Being an Aarakocra raises your Dexterity and Wisdom scores higher than you rolled them, which makes Monk all the more sweeter, but is just gravy on this steak. Monks, through the magic (?) of ki, harness their own life force to punch the ships out of dragons, and you'll be doing a lot of that my friends. Unarmored defense raises your AC to 10 + Dexterity modifier + Wisdom modifier. Focus on a Dexterity and Wisdom build for the most benefits offensively and the highest AC defensively. It's IMPORTANT that you use Unarmored Defense the best you can, because for this build you'll be ditching all of your platemail walls to hide behind, being untouchable on the sheer principle of speed. Ladies and gentlemen I present to you for your viewing pleasure... Unarmored Movement.
The Core of This Build
"Starting at 2nd level, your speed increases by 10 feet while you are not wearing armor or wielding a shield. This bonus increases when you reach certain Monk levels, as shown in the Monk table." I'm not going to post that table as anyone with a Player's Handbook should be able to read it, BUT TAKE A LOOK AT THAT. Even if you can't fly for some reason, you don't fall during your turn if you run across liquids or scale walls by running up them, making you new Falco the most maneuverable character build in Core 5e that I have ever seen. At it's highest potential, you have 80 feet of movement. But we're not done yet.
At the same level, you gain your ki for the first time, and one thing you can spend ki points on is the ability to take the Dodge, Disengage, or DASH action as your bonus action for the turn, doubling your movement while still allowing you to act that turn, giving 160 movement at it's highest potential. Additionally, I've finally confirmed that if you can Dash as a Bonus Action (As you can with Monk from Level 2) than you can ALSO Dash as your action, tripling the movement instead of doubling it. 240 Feet. Let's build that shall we? And can we do even better?
Wiki Note: The mobile feat, detailed later, is a part of this build already, and doesn't need to be added twice. It is not put in the core of the build because feats are an optional rule.
Monk class, 20 levels, Way of the Open Palm.
These allow a combination of high AC (For an unarmored character) and unrivaled speed. Play specifically for pot shots, attacking and then retreating further than enemies can reach you. Seek cover from ranged attacks, and be wary of fall damage if you fall unconscious. Seek magic items that raise AC further to help cover the gaps in your thinking where you leave yourself open. Use the Wholeness of Body Monk class feature and benefit from the sanctuary spell (From the Tranquility Monk class feature) as much as you can.
Attempt to end fights as quickly as humanly (falconry?) possible. At later levels, you will start realizing you are an unhittable genius (You might actually do that at level 4 or lower if your scores were high enough) and can punch anything to death in seconds. This is normal. Roll with it. BEWARE AOE SPELLCASTERS!!! Damage from area of effect (A.O.E.) spells can be BAD for you with this build, as all your hard-earned AC is worthless against them. Stay away from other players, at least by 25 feet (Unless you need healing, obviously) to avoid getting caught in an A.O.E. spell means either you were to close to your party, or you are doing such a great job beating the crap out of everything that you are now more of a target than EVERYONE ELSE COMBINED. This is also normal. Revel in it. If you end up appearing the biggest target, you can distract well into the group's other plans, and if you play smart enough, can completely trap enemy encounters by sheer presence, plenty long enough for your resident caster to obliterate the enemies you can't defeat. Besides A.O.E., beware groups of enemies. Monk gets a lot of attacks, but spells are usually better for dealing with mobs of enemies. NEVER let yourself get surrounded in this build unless you REALLY feel confident (You probably will at some point).
One of the major issues with this build are opportunity attacks. In addition to the above, take the Mobile Feat if used in the campaign, giving you even more movement speed (+10 feet, raising the max from 240 to 270 with Ki) and letting you bail from melee range without taking opportunity attacks as long as you've attacked the baddy on the same turn you bail. This'll also mean you can boop people! And (Even though flying means it doesn't REALLY matter) you can't be slowed by Difficult Terrain if you Dash, so nothing can stop you now! MWAHAHAHA!!!
Finally, look out for the Haste spell or a Potion Of Speed. Haste doubles your base movement speed and gives you an extra action each round it's active that can only be used for a few, limited things (One of which just so happens to be the Dash Action). With these combined factors, your base movement should be 180 feet flying, without dashing at all. Using all of your actions to Dash (3 in a round), allows you to cover in a single round a distance of 720 feet. If your party's okay with helping this minmaxing, have your local Sorcerer or Wizard take the spell for easy access to it. Otherwise, you can trade some of your base max movement by putting some levels in a multiclassing of either class to unlock the spell yourself, or just hunt down a Potion of Speed or two in case of emergency.
Trading some of that extra speed for levels in Ranger (Or other ranged classes) can make you an even greater nuisance, by allowing you to keep fighting without ever getting close enough that melee enemies can ever attack you. If you do this, go for the highest range you can possibly muster. I believe other builds on this wiki can help you with that.
Trading your race for a Thundercat (Tabaxi) will let you use its racial feat to Double your speed for the turn, making your base speed 140 feet (YES, YOU DOUBLE IT BEFORE DASHING!) so you will get 320 feet with a double dash (if you think the next turn you cant move, the rght interpetration is when you want to use this again, you just have to sit back away from everyone 1 turn, you choose when to do this)