Many of the fish we keep can be bred easily. It is a first challenge that new fish keepers take on once they become good at keeping their fish healthy. The particular way to breed a fish varies quite a bit from species to species.
You need to decide what you would like to breed, keeping in mind that 5 gallons is tiny, and then look into those fish that you like.
For livebearers, keeping the fish in a pair in their own tank and providing a hiding places for the fry is all that is needed. I breed many livebearers by simply placing a sample of a species in its own tank with a clump of java moss and going back now and then to scoop out some of the fish for sale. On the other hand cichlids typically will care for their fry so the high fry cover is not needed but most require far more than 5 gallons to breed in. Moving up in difficulty are things like corydorus that need particular water conditions and are often placed together to breed when the outdoor weather patterns reflect a rainy season. They also get large cold water changes at that time to simulate rain runoff.