A 5 gallon sounds
big but it's a very nice looking size once you actually get it set up. It doesn't really take up much more space than that bowl and the benefits of it are that the fish will be happy, and you won't have to do water changes as often.
A good filter would be the Azoo Palm/Mignon which can be found here for only $6.99. which is an amazing deal.
Also, you'll want an adjustable heater with a built in thermostat so you can set it once and forget it (still a good idea to have a tank thermometer so you can see the temperature stays constant. You can get a tank thermometer at walmart for under 2 dollars).
Trust me, once you set it up you'll love it, and it will be less maintenance than the bowl, with a happier fish. A happy healthy fish will constantly be swimming around the tank doing stuff. A fish in a bowl will start to get bored and lethargic and just kind of float in place for long periods of time. You'll want your fish to be a fish, and a pet, not a decoration! To take the best possible care of the fish, it will cost a bit in the beginning, but all of the food, chemicals, and equipment will last years.