Hi Daniel and welcome to MFK! It's good to see you are interested in fishkeeping it's a great hobby.
Fish do not grow to the size of the aquarium. Aquarium size should be chosen based on the adult size of the species you intend to keep. Having said that, fish can become stunted if kept in a in adequately sized aquarium or water quality is not maintained. I can not emphasize to you enough the importance of maintaining a clean environment and paramount in keeping a clean environment is maintaining excellent water quality. To achieve this you must have good filtration and set up amaintance schedule that includes filter maintance and regular water changes. If your water is clean and your system is clean your fish will thrive. One more thing to mention, small tanks require more diligence then larger tanks as the water can foul easier smaller tanks are less stable than larger systems so staying on top of maintenance becomes even more important as there less margin for error.
Before we make any suggestions why not tell what type of fish interest you.
I have to edit this post I thought it was 5 gallons not a half a gallon, my error. However same principals apply.