finrot worse in better quality water?

Housing
What size is your tank? 5 gallons
What temperature is your tank? 76
Does your tank have a filter? yes
Does your tank have an air stone or other type of aeration? yes
Is your tank heated? no but I might get a heater for him when my next paycheck comes in
What tank mates does your betta fish live with? One snail as of a few days ago

Food
What type of food do you feed your betta fish? Flakes..he refuses to eat the pellets
How often do you feed your betta fish? a tiny bit everyday unless a gave him more than usual, then i'll skip a day.

Maintenance
How often do you perform a water change? atleast once a week
What percentage of the water do you change when you perform a water change? anywhere from 25 percent to 75 depending on the nitrates
What type of additives do you add to the water when you perform a water change? Bettasafe and maybe a little aquarium salt or melafix occasionally

Water Parameters:
Have you tested your water? If so, what are the following parameters?

Ammonia:0 ppm
Nitrite:0ppm
Nitrate: between 5 and 10 ppm though I do have trouble seeing the difference between the 10 and 20 on the color chart
pH: ?
Hardness: ?
Alkalinity: ?

Symptoms and Treatment (most of these answered below)
How has your betta fish's appearance changed?
How has your betta fish's behavior changed?
When did you start noticing the symptoms?
Have you started treating your fish? If so, how?
Does your fish have any history of being ill?
How old is your fish (approximately)?


So a few weeks ago I finally finished cycling the 5 gallon I got and was more than happy to put my betta in it after waiting over a month.
The betta seemed pretty happy about it to. I swear he never stops moving now. always on the go and swimming. However this week I noticed his tail has gotten reallly torn up looking. I'm puzzled because before while he's had minor cases of finrot while he was in the one gallon, it was never this bad looking. I know the water in the five gallon is much better than the water in the one gallon too. He's eating normally, there are one or two minor tears in his fins I suspect are from a plastic plant I might remove soon but the back of his tail looks less like a tear and more like rot I think?

Are the nitrates too high maybe? I don't think he's tail biting. Since he's been in the new tank his top fin has actually spread out and gotten much better looking than it used to so I don't know why his tail looks worse.

tried my best to get a picture but he hates sitting still.