Yes the white scale from chin to belly is a sign of stress as well.
Also a tip, if you've got a thermometer (which he'll need for the 5 gallon with the heater because they don't always work well) then you can run it under the tap to get exactly at 78 degree's for him instead of having to wait a while. Conditioner also works instantly so you could theroretically put him right in after that but make sure to acclimate him to the new water always.
So to do that, keep him in his cup and float him in the tank if you can. Otherwise just keep him close and spoon in 2 tablespoons every 10-15 minutes until his cup is nearing full again or it's been about 45 minutes and then you can gently release him back to his tank.
For the salt here's the steps you need to take to help him. So you want to use 1 teaspoon of Aquarium salt per gallon (not just any salt!) so if he's in a 1.5 then you use 1.5 teaspoons for that ratio. And don't worry, if it happens it's actually a 1 gallon, the 1.5 won't hurt him.
• Take a small cup and put some tank water or conditioned water into it.
• Measure out 1.5 teaspoons of salt.
• Mix around in the cup until you see absolutely no more crystals (it can still burn your fish).
• Add a tablespoon of the dissolved salt into your tank every 15 minutes so your fish can adjust to it. (If he's already in the tank, if he's not in the tank then go ahead and put it all in and then acclimate him to the new water)
• Once a day do a 100% cleaning.
• Re-add in the salt you took out. Salt does not evaporate so if you took out half of your water, replace 1.5 teaspoons of salt with the above method.
• Continue this for 14 days or until all the black edging goes away.
Salt will not heal his fins, it will just get rid of the rot. So to heal the fins you can use Stress Coat conditioner (which is a conditioner in and of itself so you don't need to use the regular one) at double the dose to heal his fins.
And for the 5 gallon you can get a product called Tetra Safe Start, not always guaranteed to work but it's basically Bacteria in a bottle. You pour it all in with your fish in there, keep the lights out for the two week period and don't do any water changes for two weeks. After that period is up your tank is cycled. That's just one thing you could do for him.
If you wanted to, you could do a Silent Cycle but it involves buying more stuff. Silent Cycle is basically shoving a bunch of plants in there and you never have to worry about your cycle! Basically the plants soak everything up but it slows the cycle down and you'll never see it, hence its called the Silent Cycle. For a 5 gallon, about 10-15 fast growers would be great! Plants like Anacharis, Anubias, Java Fern, Water Sprite and water wisteria are all super easy plants that basically demand nothing and grow on their own