Please do not get goldfish. A goldfish will easy outgrow that tank; even the smaller types need 20 gallons of water each. Kept in a 5 gallon tank, they will not live longer than a few months - and their lifespan is actually more than 15 years.
A 5 gallon tank is pretty small, so keep that in mind. You will need to stock it fairly lightly if you want to have a healthy tank that does not require too much cleaning (a once a week 30% change is normal for a decently stocked tank).
Your options are fairly limited, because you can't go with anything over 2" or anything that needs to be in school, but are as follows:
1 male betta OR
2 female bettas OR
3 cherry barbs OR
3 white cloud minnows OR
2 african dwarf frogs and a snail OR
2 guppies.
Also, before you get fish, you'll need to cycle your tank... if you skip this step, your fish stand a good chance of dying. First of all, have you cycled your tank? In the wild, and in established tanks, there are nitrifying bacteria that break down toxic ammonia from fish waste and excess food into less toxic nitrates. In a brand new tank, these bacteria don't exist, so any fish in the tank will produce ammonia, which, not being broken down by bacteria, will kill or weaken the fish. So, it is vital to cycle your tank.
There are a few methods. Do you have access to an established tank? These bacteria live in the gravel and in the filter cartridge, so if you can get some from another tank, you can put the bacteria right into your tank (don't let the gravel or filter cartridge dry out). If you do this, in a day or two, your tank will beready for fish.
Another way is to get Bio-Spira. It is the actual live bacteria in a little pouch, and your tank will instantly be ready for fish. http://fishstoretn.com/bio_spira.html
Other methods, which include putting a source of ammonia in the tank and letting the bacteria build up on its own, or putting a fish in and letting the fish produce ammonia (which borders on animal cruelty, because the fish will suffer from the ammonia in the tank), take 2 to 6 weeks before your tank is ready. If you rush that, any fish you buy may die, so try one of the instant methods I mentioned above (bio-spira or gravel from another tank)