fort384 said:
Welcome to AA!
The first thing you need to do is read up on cycling a tank, and understand the nitrogen cycle.
Fishless cycling is the fastest and safest way to establish a tank.
There are not a whole lot of fish that are suitable for a 5 gal tank. A betta would be a really good choice.
Another really good aquatic pet to put in a 5 gal is freshwater shrimp.
Anyway... read up on cycling. You have some work yet before the tank is ready for fish.
Oh, and do you have a test kit? That should be your first purchase if not... long before you get any fish. The API freshwater master test kit is widely available and a good option. It will have everything you need to test bundled together. Avoid the dip strip tests... they are inaccurate and unreliable.
Fort384 has given you some very good advice. There isn't really that much to add. I just wanted to offer some more suggestions for what you could keep in your new tank.
As fort384 has said, 5 gallons is a very limiting volume. But that doesn't mean it can't be a really attractive tank.
First thing I would like to suggest is that you go get some small pieces of driftwood and enough java moss to cover most of it. Java moss is great for beginners because it gives you a natural looking planted tank without a lot of effort. The lighting you already have for your tank should be plenty to keep it health and there shouldn't be a need to add nutrients.
Oh, and you can go ahead and do all this while doing your fishless cycle. It will keep you busy while your waiting for the cycle to complete.
When you get your driftwood and moss your going to want to figure out how you want your driftwood to be placed on the tank. Try a bunch of different arrangements until you find the one you like best. Once you have that figured out look at the arrangement and think about where you want the moss to grow on the driftwood. Now just take each piece one by one and tie the java moss to them using fishing line. Don't worry, the fishing line will eventually be grown over by the moss. If you would like some inspiration do a google image search for takashi amano.
Now if this isn't the type of tank you want, don't worry about it. Set it up the way you like because your the one who's going to be looking at it. This is just what I personally like for an easy nano setup.
Ok now on to stocking.(I hope this isn't getting too long...) which should only be added after you have finished cycling.
As fort384 said, shrimp are a great option for this size tank. Also, shrimp will really I would suggest red cherry shrimp. They are easy to care for and colorful. The only problem with them is that they will breed until they take over the entire tank. But they are still probably your best bet for a starter shrimp.
If you are set on having a fish setup I would recommend you look at killifish, specifically the annuals. they can be extremely colorful and many species will do just fine in a 5g tank. Although it is worth mentioning that They are called annuals because they only live for about a year. They are also not very common at LFS. Still they are very interesting fish.
Ok, I'll stop now. Hope this has given you some ideas.
Have fun!