There's one thing that bothers me and probably nobody else about dragonborn in 5e, and that's their almost direct porting of their racial statblock from 4e. Looking at the elf, dwarf, and halfling, they get ribbon abilities with a lot of out of combat utility. The dragonborn is pretty much entirely geared for combat, and it's considered one of the weaker races for it. You get resistance to a damage type (which is very nice) and you get to breathe fire and act like a dragon once every short rest (a little less nice).
So let's give 'em some small effects they can do with their breath weapons at-will. Of course, the DM can always adjudicate for this themselves and allow such effects without the need of me telling them what they can or cannot do, these are just a few ideas.
All dragonborn can take an action to do the following effect associated with their draconic ancestry.
Acid. Black and Copper dragonborn have acid that mixes in with their saliva. While they can't burn someone with this acid, it can burn through soft materials like rope fibers and paper.
Cold. Silver and White dragonborn are able to use their innate coldness to chill objects and make certain kinds of objects quite brittle (if going by the object hardness rules, you could make those objects vulnerable to bludgeoning damage). You can also freeze liquids inside a 1 foot cube.
Fire. Red, Gold, and Brass dragonborn can use their internal flame as a firestarter, able to light torches and other small flammable objects. Not only that, you can use it to boil liquids inside a 1 foot cube.
Lightning. Blue and Bronze dragonborn can raise their voice to booming levels, up to three times louder. Also in campaigns with objects that run on electricity, they make a pretty handy emergency battery!
Poison. Green dragonborn are able to exhale some pretty putrid stuff, stuff that can irritate eyes and nostrils.