Does an aquatic frog need airation and water filtration in a 5gallon tank?

You definitely need a filter, unless you plan on doing water changes several times a week. Frogs breathe air, so additional aeration (the filter, in agitating the surface, does a great job of aerating) from air stones is entirely unnecessary, though if you find it aesthetically appealing, it certainly won't harm the frog. Depending on the species of frog, it may or may not need a heater. African Dwarf Frogs should be maintained around 75*, which may require a heater, depending on the temperature of your home. However, local frogs are well adapted to the local climate, and will be fine at the ociated temperature.