I own a 5-gallon tank and I'm getting some fish. I have had fish before. I've had things like bettas and guppies before. What fish are good for a 5-gallon tank? Do I need a filter? I have an air pump I can use if I need it. What fish would be good to have? Is there any that can be put with others?
A single Dario is the only fish I can think off. But it deserves a heavily planted tank, upon which you hardly see your fish as it lives fairly stationary within plants, moving from time to time. I enjoy spotting it, watching its fins move like wings of a hummingbird, trying to spot a tiny critter that is passing by. It also deserves live foods; it won't go after flakes or pellets. A filter with low current is highly recommended; a heater not required. The picture in my avatar reflects this setup, although plant-mass is currently significantly larger then when this image was taken, and houses a single Dario (you won't spot it in the image ); this Dario will move to a larger tank soon as it is part of my breeding scheme.
There are very few fish that will thrive in a five gallon tank. Although a betta will do OK in a 5 gallon, it will do even better in a 10 gallon or larger.
Since you do not have anything other than the tank and an air pump, I would strongly advice you to get a larger tank if at all possible. You will need some type of filter. Since you have an air pump, you could get an internal sponge filter. They work quite well, but take up a lot of room in what is already a small tank.
Many small fish like danios, rasboras, neon tetras, ember tetras, etc. are fine for a 10 gallon tank, but because they like to be kept in small groups of 6 or more fish, a five gallon tank is rather small. Thus, if there is any way you can upgrade to 10 gallons or larger, you significantly increase your options.