I have experience with axolotls, african dwarf frogs and a few species of african clawed frogs.
Axolotls are definitely not an option for you - you need a two foot tank minimum for one, 5 gallons is not even close.
African clawed frogs, regardless of species are not an option - a 10 gallon tank is minimum for one frog of most species.

For african dwarf frogs, you could have a pair in this tank if the conditions are properly met.
Sand substrate or no substrate. Avoid gravel.
LOTS of hiding places and fake plants - use silk plants, not plastic. Plastic is quite rough and can tear the webbing between their toes.
These are very shy creatures by nature, so the more hiding places you have around, the safer and braver they will feel.
Temperature should be kept in the high 70*s F.
Filter your water with a gentle filter. Water quality is very important and you need to filter and cycle their tank the same way you would for fish. Google "Fish-less cycling" and do lots of reading and familiarize yourself with the Nitrogen cycle (ammonia - nitrite - nitrate) and it's importance in the aquarium.
For food, do not feed anything freeze dried because it can lead to constipation and do not feed any type of feeder fish, ever. Feeder fish are kept in awful conditions and are nearly always diseased - it only takes one sick feeder to infect your entire system. Feed them sinking HBH frog and tadpole bites (found in every petco, petsmart and most other petstores). Treat them with frozen bloodworms (defrosted prior to feeding) about once a week if you want, you don't have to.