Well, like I said, Rogues also get 5d6+ability modifier when Sneak Attacking with a shortbow.
Rangers can use a longbow and attack twice for 1d8+ability modifier each time; Colossus Slayer adds another 1d8 or Horde Breaker adds 1d8+ability modifier. With Archery Style, the average DPS winds up being more than 5d6+ability modifier. And I haven't even included Hunter's Mark or the revised Favored Enemy yet.
Fighters are similar, but instead of Colossus Slayer/Horde Breaker they have to use Superiority dice and/or Action Surge, which are limited resources. But they do have quite a few (5) of those dice. They also get an additional ASI which boosts their DPS noticably.
Warlocks use Eldritch blast and Agonizing Blast for two 1d10+ability modifier bolts. This is a bit weaker... unless they have Hex up, in which case it's again more damage than 5d6+ability modifier. And of course, Warlocks are full casters with attack spells on their list, so those are available on a limited basis.
So the Gunsmith deals nice damage, and it's especially nice that there aren't requirements to fulfill (like Sneak Attack or Colossus Slayer) or resources to expend (like Superiority dice). But the damage isn't any greater than what other ranged classes can do, and unlike those classes the Gunsmith doesn't get options to increase that damage further. A Battlemaster with a longbow can nova for basically 8d8+quadruple ability mod, which is more than 2.5x more damage than anything the Gunsmith can do. A Warlock can cast Blight for 8d8 (save half).