Ok stop. You won't be adding fish for a while yet.
As for your list of fish - well I'll get to that in a moment but I'll just start off by saying that you should never listen to your LFS. ALWAYS do your own research first.
Seeing as you are here, I can immediately see that you want to do what's best for your fish so please, please, believe me when I say there's a lot more to fish keeping than your LFS is going to admit to.
Firstly, 5 gallons is small. Small tanks aren't as stable as larger ones are. For example, the temperature can change very suddenly in small volumes of water. You need to keep this in mind and remember that fish are very sensitive to changes in their environment. Because of this, it'll be harder to maintain than a bigger tank would be. Just keep this in mind. You can't cut corners with fish-keeping.
I would begin by reading through all the links in my signature but I'll sum it all up for you here anyway.
The first thing you need to do is set up your tank with de-chlorinated water and let it run for a couple of days. Make sure everything's working ok. Then go buy yourself a bottle of pure ammonia. Household ammonia used for cleaning will do but make sure it has no additives or anything as this'll make your water toxic to the fish you'll be addin in about 6 weeks - yes, 6 weeks.
You see, first you need to get your tank cycled. The best way is to add a small quantity of ammonia to your tank daily until the ammonia and nitrIte are at 0 and the nitrAte is high. This takes about a months. You'll need to buy a test kit for ammonia, nitrIte and nitrAte. A liquid-based one is best and most accurate and will last longest.
If you aren't already aware of what cycling is, I'll go through it quickly here. Basicaly, fish produce waste. This waste contains ammonia. Ammonia is very toxic to fish and will kill them. Luckily, there are good bacteria that change ammonia (they sort of eat it) and change it to the slightly less dangerous nitrIte. NitrIte, however, is still deadly. Fortunately, nature has a solution to everything. There are good bacteria that change this lethal nitrIte to nitrAte. NitrAte isn't as deadly. There are no bacteria to change this in your tank but all it takes to keep the water clean is a single partial 20-25% water change with DE-CHLORINATED water once a week. I do mine every Sunday...
Anyway, using DE-CHLORINATED water is key. You see, chlorine found in tap water will not only burn your fish, it'll also kill all the good bacteria - a great waste of those 6 weeks of fishless cycling...
If (and when) you buy a test kit and start adding ammonia to fishless cycle your tank, you'll notice the ammonia goes up as you add more and more ammonia every day and it begins to build up. Eventualy, you will notice the readings start to drop as the good bacteria start to grow. Soon enough, nitrIte will start to go up but ammonia will continue to go down. You have to keep adding the same amount of ammonia every day. You will soon see that ammonia and nitrIte are at 0. NitrAte will be very high. Your tank is now cycled.
Do NOT confuse this cycling process with fresh water from the tap - tap water should have a reading of 0 for ammonia and nitrIte and will sometimes contain some nitrAtes - HOWEVER, it does NOT contain the good bacteria - a tank has to go through the process I described above to be considered 'cycled' and safe for fish.
You need not do water changes during a FISHLESS cycle.
At this point, you can add fish BUT you have to do a 90% (or as much as necessary) water change first. The reason for this is that you don't want to put new fish in a tank with very high nitrAtes. In fact, you should strive to always keep the nitrAtes as low as possible. Under 40 is good, under 20 is best. If you don't over-stock or over-feed and do a weekly gravel vacuum (buy a gravel vac.) and partial water change, this should be easy.
When you do add fish, you can stop adding ammonia. The ammonia was there to feed the good bacteria that change ammonia to nitrIte and then nitrAte so that the bacteria are already there when you add the first fish. These first fish will now produce the ammonia you need to feed the good bacteria by producing waste. Keep in mind that rotting leftovers and debris also produces ammonia so make sure you vacuum up un-eaten food and don't over-feed your fish.
Because your tank is only 5 gallons, you will want to add only about one fish at a time. That way, the good bacteria have time to multiply and adjust to the new amount of ammonia before you get more fish. If you suddenly add too many fish, especialy in a small tank, you can cause what is called a 're-cycle' and this will likely poison and kill your fish. About one fish every week is a good guideline.
Always make sure you monitor your water parameters - your ammonia and nitrItes when you have fish in the tank must ALWAYS be at 0. Any more is considered toxic and can kill your fish and will deffinately damage them. Bad water quality also stresses your fish and makes them susceptible to disease. NitrAte should always be under 40. Try to keep it under 20. If any parameters get out of hand while there are fish in the tank, a water change (always partial with DE-CHLORINATED water) will help lower them and bring them under control.
What else? Ah yes. The good bacteria live in your filter media (sponges, floss etc in your filter) and in the gravel and ornaments in your tank. They DON'T live in the water. The significance of this is that you can get bacteria from an established, cycled tank (one over 3 months old) by borrowing some gravel, filter media or even ornaments. A piece of filter media is the best method. Put it in your own filter and add bacteria food (ammonia) and you get an almost instant cycle (no 6-week wait). However, you need to make sure the tank you take this from is healthy (you don't want to introduce diseases) and you need to keep up with feeding the bacteria (add ammonia daily) and monitor the levels to make sure everything is stable until you add the first fish. Again, only one at a time.
The other significant point about the bacteria's choice of home is that you cannot EVER use tap water to clean out your filter. Once in a while, you may find your filter gets clogged up. When this happen, do a water change (DE-CHLORINATED water as usual of course). The water you take out from the water change you will use to gently squeeze and rinse out the filter and filter media in. This water will not contain any chlorine so you can safely clean out the filter without destroying too many good bacteria. Once in a while, you may also notice parts of your filter media are beginning to - well - biodegrade. When this happens, buy a replacement but replace the media over a period of several weeks. Take out part at a time and replace it slowly. That way you aren't removing all the good bacteria at once.
Also note that you can use fish food to fishless cycle as the rotting food will produce ammonia. However, this is quite a bit more messy than cycling with pure ammonia and probably slower and more expensive over-all.
You may have noticed that fish-keeping is a lot more to do with bacteria than to do with fish but your choice of fish is still essential to their well-being.
Let me make something clear - keeping fish is not about just 'keeping' them - it's about giving them an environment in which they can thrive and be themselves. In the wild, a tetra has a whole river and a huge school of it's own kind to live with - keep this kind of thing in mind when choosing fish and don't cram them into a small space for your own enjoyment - they are living, feeling animals and they deserve the best you can offer.
I'll help you out with a simple guideline that puts stocking in perspective. Basicaly, there's a guideline often used amongst aquarists that states 'one inch of ADULT fish per US gallon of water'.
The ADULT part of this is essential - even a 12 inch oscar started out as a tiny (under an inch) fry, so did a 12 inch bala shark, a 24 inch osphronemus goramy, a 12 inch piranha, a 3 inch cory cat, a 4 inch bristlenose pleco, a 1 inch neon tetra, a 6 inch moonlight gourami or a 1.5 inch male guppy. What I'm trying to say is that you cannot judge a fish on the size you see it at in your local fish store - it could grow to be a 30" monster for all you know.
I also advise against taking advice from LFSs when it comes to stocking numbers because all they realy want is to maximize their profits by selling lots and lots of fish.
Anyway the one inch per gallon guideline's only a guideline and more experienced fish keepers will exceed it but you need extra filtration, lots of plants and experience to do this. Similarly, the guideline won't work for fish that grow to over 4" and you can't keep any fish over 2" in a 5 gallon. Lucky for you all the fish you mentioned grow to about 2". Unfortunately, tetras and rasboras are schooling fish (something else this guideline doesn't account for) which means they need to be in a group (of their own kind) of 6 minnimum... Well, do the maths: each rasbora and tetra grows to (approx.) 2", you want 3 different species, each needs to be in a group of 6 = 2 x 3 x 6 = 36... That means you need a 36 gallon tank MINNIMUM for those fish... Also take into account the fragility of neon tetras. They need a mature tank with steady parameters. A 5 gallon tank is rarely stable enough - especialy if newly set up - to be over-stocked with such fragile fish.
The 2 male fancy guppies were a better choice. I suggest you get 2 male fancy guppies and a (male) platy to begin with actualy. That's pretty much the capacity of your tank. You might be able to add a couple more (male) platies or a couple of honey gouramies later on but you should start by adding a single male guppy (after fishless cycling) and see how things go from there.
There's probably a lot more that can be said and I'm sure I've left a lot of stuff out and other people have probably beat me to answering anyway but nevermind

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Good luck! Oh, and read those links in my signature
