The hardest thing about doing it is keeping the water clean. That means no ammonia, or nitrite, with as little nitrate as possible. It is possible if you put in the effort. The nice things about larger tanks is there is more water volume to dilute the pollutants. With smaller tanks, and with more than a single fish, that means more bio load, and more work for you. Or you risk disease and death of your fish. If you are willing to put in the effort, a 5 gallon can make a great home for some of the micro fish in the hobby.
EDIT:
Some people's knowledge on fish are constrained to the fish that their local Petsmart carries.
Chili Rasbora are fine for a 5 gallon
CPD are fine for a 5 gallon
Bumblebee goby are fine for a 5 gallon
Dario dario are fine for a 5 gallon
Dwarf puffers are fine for a 5 gallon
Platium barbs are fine for a 5 gallon
The list can go on and on. Not all of these are suited for a beginner, but some are just as easy to keep as guppies, in a 5 gallon tank.
**************Name calling? Really??