Suggest a great filter

find a filter at your lfs that is the proper size of your tank. sorry but I dont know what brands your lfs carries.

AquaClear Mini. Probably tons of filtration for a 5g, but a great product.

It would be better if you could let us know what you have available at your LFS. Then we could probably tell you the best from that range.

good point

You can help your tetras avoid getting sick by doing a partial water change each day. 20% a day on a 5 gallon isn't much work for you but will mean a lot for the tetras.

Then I would suggest a small HOB filter like the AC Mini or Whisper 5-15. If such things are not available then a small box filtr run with an airpump will also work.

Welcome to AquariaCentral!

5 gallon tanks are very limiting in terms of stocking fish... personally, I would suggest a 15+ gallon tank for any school of small tetras. If you're willing to spend a few bucks, go out and grab a larger tank... your fish will thank you for it, and you'll have an easier time maintaining the tank.

However, if you want to keep your 5 gallon tank, I would get yourself a good filter with lots of biofiltering capacity... that should help your tank out a bit. Grab yourself an Aquaclear 150. Since AC filters have the ability to adjust their outflow, turn the filter down to minimum flow. That should reduce flow to about 50gph, which should be just fine for just about any tetra species. I suggest the 150 over the mini, because it has a larger biofiltering capacity, and it should help increase your tank's water volume by a little bit.

It also sounds like your tank hasn't cycled yet... grab yourself an ammonia and nitrite testing kit, and read the threads in this forum about cycling a tank.

HTH
-Richer

A whisper 5-15 would be perfect for a 5 gallon tank. And YES, it is needed...

I'm changing my vote to the AC150 which Richer suggests. You can turn it down for now and when, yes when you decide to get a bigger tank, you'll have your filter already.