First thing I would check is that you have been doing the nitrate test correctly. Nitrate bottle #2 in the API test kit needs to be shook and banged on the floor. I use my knee. This is because the 'crystals' settle at the bottom or something. Basically add bottle # 1 then shake test tube then add #2 and shake again then let stand for 5 mins.
If nitrates are definitely 0ppm then your tank is not cycled. In order to do this you need an ammonia source. The fish you put in would have provided this, however gold fish produce way to much waste for that size of tank and 5 of them must have caused a pretty big ammonia spike and killed the fish. Now you need to keep ammonia going in to the tank to build up your bacteria colonies.
Buy some pure ammonia with no other ingredients and dose small amounts until you have a nitrate reading. When you are getting nitrates. Add 4ppm of ammonia and see how long it takes before they reach 0ppm, when this is less than 24hours you should be cycled. Provided you have no nitrite and a nitrate reading. Weekly water changes at 25% will keep nitrates from going above 40ppm.
Alternatively you could place some fish flakes or raw shrimp in a mesh bag in the tank and let it decompose, this will give ammonia.