Please help me build the best DPR monk at 5th level.
Point buy stats, human and half elf are the only racial options.
Mono-class monk, no dips into other classes.
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For max DPR, you should be a variant human with the Savage Attacker feat. This is because you only rely on 1 stat (Dex) for DPR, so you can afford to spend a feat - and Savage Attacker is the only feat that directly increases DPR. When attacking with a d6 damage die, you should reroll results that are 3 or less. Anydice link demonstrating the results of rerolling different minimums here. Note that this give an average damage of 4.25; we will use this result later.
Obviously, you should make sure you have a 16 in Dex. After that, all other stats won't affect your DPR, although you probably want to have a 16 in Wis and a 14 in Con (or vice versa). Your ability score increase at level 4 should be used to raise Dex to 18.
Putting it all together, your standard unarmed attack will deal 1d6 + 4 for an average of 8.25 (with Savage Attacker).
A round where you spend no ki points deals [1d6 + 4] + [1d6 + 4] (Extra Attack) + [1d6 + 4] (Martial Arts) = average of 24.75 damage.
A round where you spend 1 ki point to use Flurry of Blows deals [1d6 + 4] + [1d6 + 4] (Extra Attack) + [1d6 + 4 + 1d6 + 4] (Flurry of Blows) = average of 33 damage.
Just a first pass and not considering feats.
Best DPR is going to come from a DEX focus as it allows use of the light, finesse shortsword. The only monk weapon that does more damage is the Greatclub (1d8 vs 1d6) but this is more than offset by the extra attacks
Assign 15 to DEX, if you choose human this will raise to 16, if you choose half-elf choose to raise it to 16. Without feats, use your ability increase at level 4 to raise this to 18.
Choose Way of the Four Elements with Fangs of the Fire Snake.
Round 1 (5 Ki available)
Round 2 (2 Ki available)
Round 3 (1 Ki available)
Round 4 + (0 Ki available)