Sadly enough, I don't think there's any way to answer this. D&D is way too variable. For example, as soon as you said "assume every attack hits", any ranger using the sniper feat jumped up 20 damage per round between levels 7 and 10. Is this a Hunter shooting on a wounded target? Is it a Beast Master hunter? There's just too many variables, I feel.

@Theik What's a beast master hunter? Also, some of these other issues can be answered; we can assume that the ranger is the only one damaging the target, meaning that the first hit won't be against a wounded target, but the second+ attacks are (if we assume one enemy who is a bag of hit points, being grappled by the barbarian so it can't attack the ranger) - in fact, was making the archetype open to the audience a mistake? Should I enforce an archetype like I was originally planning?

I feel like it is answerable. However, the question needs to be about a specific level, not a range or levels, and it needs to specify which sources we can pull from: whether we need to consider the Ranger's various UA incarnations may be the deal-breaker in terms of broadness.

"assume the race to be Wood Elf for that +2 DEX and +1 WIS (or a similar race well suited to this role" does that mean only Wood Elfs, any race with the same ASI, or any race suited to maximizing damage?

@Ruse I have restricted this to level 8 (see my included justification) and have specified no UA. With this, plus my note about the Colossus Slayer as prompted by Theik's comment, do you think this question is now good to go?

@Ruse I meant the last option; if someone can suggest a race that would be better suited than a wood elf, by all means; the wood elf was just my suggestion based on ASIs

Also note that I'm expecting the Sharpshooter feat to be a part of this build, but if answerers show their working, this +10 can be excluded and the totals recalculated easily enough. On the other hand, if someone can beat that without using Sharpshooter, that might be interesting to see (for example, someone might come up with an unexpected GWM build or something)

The second to last point (the one you just added) heavily implies there is only one enemy. Just point it out in case you don't intend that to be a restriction. And yes, seems answerable now.

@Ruse I'm going back and forth on it, but I'm concluding that I do want this to be a restriction; I'll try to make that more explicit

When you say every attack hits and no critical hits, does it make feats like Lucky and Great Weapon Master (first point) irrelevant for increasing DPS? When you say no spells, does it make Magic Initiate useless too? Can we assume that opponent does something every turn like leaves our reach for opportunity attacks or casts a spell for Mage Slayer? What about abilities which require saving throw?

And if enemy is being grappled, does it means that as soon as we knock him prone, it is advantage time until the end?

@NautArch Correct, I'm looking for average, not highest. Ruse's answer seems to be using average values, so if I update my question to make that explicit, it shouldn't invalidate that answer, but I've asked to be sure (I'll update once I get confirmation from Ruse).

I'd also try and see what language there is to get a 'normal' value

Would average DPR work?

@NautArch Does the last sentence I've just added to my question resolve this? I've used the term "average damage" (since I've specified 5 rounds, I'm not sure if DPR might sound a bit weird...)

@NathanS I assume you are using these calculations in an attempt to balance your homebrew ranger class? Because as it stands, the answer doesn't really come even close to being an average encounter anymore, I don't think the go-to build for any ranger in existence is a ranger specifically optimized with the assumption that you can't miss or crit. :P

So trying to extrapolate some sort of damage per round to balance your dragon companion around is going to be... iffy.

@Theik True, I was planning on using this as an upper bound; I want to be able to find a dragon that's lower than this, not that matches this, with regards to DPR. But at this point, I'm at a loss with how else to approach balancing my ranger archetype (without just reskinning the beastmaster, as you proposed before, which I'm still reluctant to do as it seems like admitting defeat).

I think the problem you're facing is exactly the same reason why the beast master is underpowered in the first place, it's extremely hard to make a character balanced when it's essentially two characters. You have to somehow make a creature that is not too weak that it's essentially pointless, yet not too strong where it overshadows other options, while also trying to balance other concerns about now controlling 2 entities at the same time.

Wizards opted to go for the safe route of "if it's too weak, that's less of a problem than if everybody feels it's the only viable ranger option" I think.

@Theik Ultimately, whatever I come up with will have to be playtested a lot to see how it fares, ideally in parties with other kinds of ranger, as well as non-rangers, to see how everyone else in the party feels with regards to their contributions during combat.

That's usually the smartest approach for homebrew, honestly. You can theorycraft it until the end of time, but there's always going to be something you overlooked or didn't think about. If the ranger feels it's a cool concept and nobody else is bothered by it being overpowered, at the end of the day, it really doesn't matter if it is balanced or not.

But I hope you manage to find the answers you're looking for. :) Good luck!

@NathanS I...don't think so? That's asking for the average value of damage while I was trying to say that you're looking for the average damage overall. In that this shouldn't be measured against a crazy optimized build.

Becasuse I'm pretty sure that 85/round is pretty above average.

And if you make a class that can actually easily deliver that amount per round and do it consistently, then no one will pick any other class if you're playing in an optimized game.

@NautArch As I said to Theik, I was going to use this as an upper bound. I wanted to see just how much damage (average, not max) a well optimised ranger can do, but I don't want my dragons to be able to match that, since as you say, that's above average. I admit that this is different what what I was originally going for, and I'm essentially trying to extract value out of asking the wrong question, but at this point I feel like I just need to go away and try to figure this out by myself...

Maybe once I've come up with something I feel is balanced, then I can come back and essentially reask the currently closed question (I might as well delete that one, it has no answers and clearly won't be reopened, despite the meta question), but with a specific pair of dragon stats in mind; rather than asking "which dragon stats would work?", I'd be asking "do these dragon stats work?" - that's essentially what I did with the pseudodragon aspect of my archetype.