Something seems fishy here, and there's not enough information provided to know exactly why.
Let's say you're a 5th level Battle Master Fighter with Sharpshooter. Proficiency bonus of +3. If you chose Fighting Style Archery, you'll have another +2. If you have a 20 Dex (I'm assuming this just for the sake of discussion) +5. That's a +10 to hit at 5th level. At 5th Level you have two attacks per round, and in one round per short rest you can have three attacks.
If you're using a Longbow, that's 1d8+5 damage with a range up to 600' due to Sharpshooting. If you take your -5 to hit, this damage becomes 1d8+15.
So now let's math.
No Sharpshooter
Every round: +10/+10 1d8+5/1d8+5
That's two attacks at +10 each doing 1d8+5 damage. If you're going against something with an AC of 15, you'll hit on 80% of your attacks. Each attack has a low damage of 6 and a high of 13, with average being 9.5. That means, on average, if you hit on every attack in a round, you'll do 19 damage that round. But you only hit 80% of the time, so let's apply that to your damage. 80% of 19 is 15.20, so against an AC 15, you'll average 14.20 point of damage per round if you're not using Sharpshooter. But occasionally you'll hit a critical and you'll average 14 damage per critical. So including that brings your average potential damage per round to 15.65 without Sharpshooter. Action surge rounds would average 23.475 damage in that round.
But what if you are using Sharpshooter?
Every Round: +5/+5 1d8+15/1d8+15
Two attacks, each at +5 each doing 1d8+15 damage. If you're going up against something with an AC 15 you'll hit on 55% of your attacks. Each attack has a low damage of 16 with a high of 23, with average being 19.5. Bippity boppity boo, average per round damage of 21.90, including the occasional critical. If you action surge that goes up to 32.85 for an average.
If you hit on all three attacks (thanks action surge!) and they're all criticals and they're all max rolls and you used sharpshooter... 93 damage.
That's 2d8+15