I have to agree, 5 gallons is WAY too small for a goldfish. Fancy goldfish average 8 inches at full grown and they do this quickly when healthy. Goldfish are also about the dirtiest fish there is.
As was already stated, test strips are VERY INACCURATE and I would not rely on those results. If that is all you have to test with, maybe taking a water sample into the LFS and asking them to write down EXACT numbers and name of the kind of test kits they used, and bring us your results.
The symptoms you are describing are common with high ammonia levels, warm temperatures, and overall, tanks that are too small for the fish that is in them. The red veining in the fins is a warning sign, and I can predict that even if you did a 100% water exchange every day, there are still going to be problems with keeping this fish in a 5 gallon tank for more than a few weeks. Goldfish consume much more oxygen than a standard fish, and warmer temps will mean less oxygen levels. A high ammonia level on top of this will only add to the problems.
Besides the other info that was asked for, I am wondering how often and what foods you are feeding your fish? How much at a time? And, what kind of a filter are you running on the tank?
The best thing for you to do is to get accurate test results and then either move the fish to a much larger tank or find it a new home. Unfortunately, that is really about the only solution to the problem. For one fancy goldfish to get to full grown safely, expect to need 75 gallons. Most goldfish, if healthy, will reach full grown within the first 3 yrs.