Fin condition in bettas is strongly tied to water condition - you need to perform 25-50% water changes weekly in a five gallon, depending on your test results.
Pick up an API master kit and learn how to use it. It's invaluable in helping to determine your water parameters.
Vacuum the tank, perform a large (75% or more) water change since your small, infrequent changes are probably leaving quite a bit of undesirable material behind.
Bettas also do well in warmer water. You can kick the heater up to 78-80, which can relieve stress in some bettas. After your water change, you can add a little AQ salt.
Biggest factor in healing will be water quality. Keep on top of it and you shouldn't have to do much, if anything else to help him out.