Hello; You are some distance from a good fish store. I am as well. Here is a method I have used many times over the years. This assumes that the tank does not need to be cleaned. I set up a new tank by first filling it with water to see if it is water tight. If it holds water for a day, I then drain (siphon; do not try to move a tank with water in it.) as much out as possible. (This dillutes any contaminants that may have gotten into the tank over time. You can also give it a rinse if you want.) I then set it on the stand where it is going to stay and level the tank and stand before adding more water. Try to pick a place that will not be damaged by water as the water will spill eventually. (I also put some thing under the stand legs to prevent the legs from pressing into the floor. I have used furniture coasters and empty cat food cans.) Rinse the new gravel and put it in the tank. Fill the tank with water and set up the heater, light and filter. If you do not have the chemicals handy to treat the tap water for chlorine, you can let the tank sit empty of fish for a week with the filter running. This will allow the water company stuff to dissipate. (I keep tap water in containers sitting around for a week or two to use for water changes. I leave the tops open to the air and in warmer weather put a little plug of foam rubber or a cloth held on by a rubber band over the openings to keep the mosquitoes out. I havent used the chemical chlorine treatments in years.) If you can get the chemicals, treat the water as directed BEFORE adding it to a tank with fish.
I almost always have some floating live plants on hand and add some a day or two after filling with water. Plants are not necessary, but I like them and feel that a tank is better off with live plants. After a week or so and assuming that you have not gotten access to a test kit and the ammonia mentioned, there is a way to add fish. The water should look pretty good by then and be fairly clear. If not, it may not be wise to proceed.
Based on what I have read on this forum, you can at this point put some of the water from the established five gallon and perhaps hang the filter medium in some way. (If it is dirty the folks on this forum suggest rinsing it in tank water, not tap water. This does make sense.) You could also put some of the gravel from the five gallon in a porous bag of some sort. Perhaps a bag made from the plastic screen door material, I have used this stuff before. Or just some ornament from the five gallon. I think the idea is to have something from the old tank with beneficial bacteria on it when you add fish.
I will add a single fish such as a zebra (Zebras are hearty and can tolerate a range of water conditions and temperatures. Also you have some zebras.) I like to put the fish in a bag with water from the tank it is in and float the bag in the new tank for enough time that the temperatures are the same or within a couple of degrees. I then open the bag and let a little of the new tank water in. I watch the fish very closely for a while and if all is ok, I add some more. With the mix around 50/50 and the fish doing ok., let it lose and keep an eye on it for a day or two. After that I slowly add a few more fish each day or so.
You must have decent tap water as the fish in the five gallon have done well. Good luck. If you get access to the chemicals and a test kit, I imagine someone on the forum will guide you thru their favorite proceedures.