Frog feces is quite toxic to fish. It is not recommended to mix frogs and fish. Especially in a tank as small as 5 gallons, the frog waste can pollute the water quite quickly. Also if you did not cycle the tank the frog xcould have died of nitrite poisoning. Betta might have tolerated it better.
Get a nitrite test in stead of new fish right now. Do not get anything else in the tank before it is cycled. Change water immediately and then very often if test shows there is nitrite.
Corydoras should not be kept alone. They like the company of their own species so at least 4 in small tank and preferably 6-8 is there is more room.
Some little corydoras could make it in your tank (once cycled), like pygmy corydoras.
Neon tetras are schooling fish so it adviceable to get 6-8 individuals at least, but your tank is too small.
Good luck with the hobby and hope the betta is ok.
