#461.5 damage total, 85.5 damage on most rounds

###Feat selection

Given that we assume all attacks hit, any serious attempt must include either Great Weapon Master + Polearm Master or Sharpshooter + Crossbow Expert so at to maximize the number of attacks and the damage on a hit. None of the many reasons we would favor the SS+CE over GWM+PM (Archery Fighting Style, lack of heavy armor, Elven Accuracy etc.) matter given our restrictions, so we choose GWM+PM because of the slightly better weapon damage dice.

###Race selection

Given that we are using GWM+PM we need a race that can improve strength. Whether the race improves it by 1 or 2 is irrelevant because we can choose either 14 or 15 point buy so our starting strength modifier will be +3 regardless. Among such races, there are several with have an offensive trait that might improve melee damage.

- The Dragonborn's Breath Weapon and the Simic Hybrid's Acid Spit simply can't compete with a single GWM attack.
- The Fallen Aasimar's Necrotic Shroud (even when applied over the course of 4 consecutive turns) can't compete with two GWM attacks. 
- The Half-Orc's Savage Attacks is irrelevant given our restrictions. 
- The Centaur's Charge, the Longtooth Shifter's Shifting Feature, and the Minotaur's Goring Rush can't compare to a GMW attack. 
- The Bugbear's Sneak Attack deals an extra 2d6 at the beginning of combat, assuming surprise.
- The Variant Human's Feat allows us to enhance strength for +1 strength, which deals 15 extra damage over the course of 5 turns if we assume 3 attacks per turn. 

Hence, Variant Human is our chosen race.

###Subclass selection

None of the Ranger's subclasses provide offensive features at level 7, so we need only compare the level 3 offensive features. 

- The Ranger's Companion and Planar Warrior cannot compete with GWM's +20 damage, so Beast Master and Horizon Walker are out. 
- Colossus Slayer is strictly superior to Slayer's Prey given that we already have a use for the bonus action and that 1d8 is larger than 1d6, hence Monster Slayer is out.
- Horde Breaker is useless because we are facing a single enemy, Giant killer is also useless because the Barbarian is soaking all the attacks, and Colossus Slayer's additional 5d8 is inferior to the additional attack from Dread Ambusher.

Hence, Gloom Stalker is our only option left.

###Build

In this case, partly because we had few things to consider and partly because some of the restrictions heavily favor some choices over others, we managed to narrow down to a single build. 

This means that, even without making making the full damage calculation, we can be reasonably certain that the combination that deals the most damage under our restrictions is a Variant Human Gloom Stalker with Great Weapon Master, Polearm Master, and +2 strength ASI.

##Damage calculations

The total damage over the whole combat is `[rounds] * ([action attacks] * ([weapon dice] + [GWM] + [STR]) + ([PM dice] + [GWM] + [STR])) + ([weapon dice] + [GWM] + [STR] + [Dread Ambusher]) = 5 * (2 * (1d10 + 20 + 4) + 1d4 + 20 + 4) + (1d10 + 20 + 4 + 1d8) = 5 * 85.5 + 34 = 461.5`.

In that calculation I have not included reaction attacks. If we can guarantee an opportunity attack each round, then the total would be `5 * (90 + [weapon dice] + [GWM] + [STR]) = 5 * (90 + 1d10 + 20 + 4) = 5 * 119.5 = 609`.