Off the top of my head, there are a few salient issues I would need to address, or be prepared to address:
* Firearms are LOUD. What's more, if you're planning on delving a dungeon, firearms' natural tendency towards high decibel levels is going to be amplified by the fairly close quarters and hard surfaces inherent in such a milieu. Fortunately, "Tactical Shooting" covers this: -5 to hearing rolls for (20-HT) minutes after a firefight. Unfortunately, the odds of permanent hearing loss are pretty high (delve often enough and you're going to critically fail the recovery roll at some point). More bad news for our TL 5 delvers is that hearing protection (or at least, "mundane" hearing protection) isn't really available. Which isn't to say the party's magician can't brew up some more arcane assistance in that area. If using the standard magic system, Vigor (from the Body Control school, to grant +HT) and/or Restore Hearing (from the Healing school) are going to be staples. Keen Hearing (from the Mind Control school) might not be a bad idea, either. If using Ritual Path Magic (which I would love to do), anything in those same veins will be useful, as would some sort of "protect hearing" ritual. TL 6 delvers might have access to sound suppressors, at least for some weapons.
* Dungeons aren't known for being well-lit. Firefights are likely to ruin the light adaptation of everything still standing at the end of them. The good news for TL 5 delvers is that there are some decent mundane options for light-sources. If the delvers are TL 6, they can even get their hands on electric lights. Obviously, magical illumination will be valuable.
* Dungeons are stereotypically close-quarters environments. The odds of engaging at distances of more than, say, 30 yards are probably not great in the usual dungeon. Characters had better be able to handle themselves competently in melee, or have buddies who can plug the line (just don't shoot them in the back!). Fast-Draw (Ammo) is going to be a big dealor Fast-Draw (Pistol) if a character is taking the New York Reload approach and carrying several loaded firearms (particularly for early TL 5).
* Certain types of monsters (corporeal undead, golems, anything that's homogeneous) have quite a lot of resistance to piercing damage! For shooter-heavy parties, these encounters might be especially dangerous. PCs better be prepared (and able) to employ alternative measures against such targets. Having competency in slashing or crushing weapons, magical damage-dealing in general, or other options (explosions!) will be necessary if such enemies are expected.
* Explosions! TL 5 may only have blackpowder available, but blackpowder still goes boom, and nothing but common sense is stopping delvers from packing a satchel of 19th-century hand grenades (HT.190, for example)and for TL 6 delvers, there's a whole smorgasbord of explosive options: TNT, dynamite, nitroglycerin, and more "conventional" hand grenades of the concussion and fragmentation varieties. Dungeons seem like they might not be the wisest place to employ such equipmenthopefully PCs would be aware enough to remove themselves from any potential blast area in advance, particularly given the close confines, but there's also the danger of collapsing the place.
In addition to those issues, there are a few more that I'm less sure of how they might be handled approached:
* Ricochets. Striking a hard surface at a sufficiently oblique angle is a recipe for unpredictable trajectories. How would this be modeled?
* Shotguns. Are they useful? I could see a delver grabbing a Colt Model 1855 (or an FN-Browning Auto-5 at TL 6) and loading it with slugs, but even then you'll probably get more mileage and pain-output from a Spencer or a Mauser Kar98k. Do Shotguns have a place outside of going hunting for razorbats?
* What are the adversaries doing amidst all this technology? Are goblins and orcs regularly packing heat? How would this impact encounters with other foeswhether dragons, gladiator apes, trolls, ghosts, etc.?
* If I'm a TL 5 adventurer armed with my pair of Colt SAA revolvers and I'm going into a Dungeon Fantasy delve (and honestly, even if I'm a TL 6 delver), I'm going to be wearing at least a steel breastplate and a helmet. The may not stand up to many firearms, but I'd rather have them than not if a gladiator ape jumps on me from the alcove. Are you armoring up? Why or why not? What makes sense for the various roles to be wearing.
* What other possible issues am I missing or not considering? What would change at TL 6 instead of late TL 5? (Semiautomatic handguns, SMGs, and LMGs, of course. But what else?)