i have a 5-gallon tank

Question
i wanna know how many goldfishes can i have in my 5-gallon tank..

Answer
The correct answer would be none. Let me explain. Goldfish or Carassius auratus can reach up to 2 feet in length and they have a lot of girth as well. These fish are cruelly treated every day by thousands if not millions of people who put them in bowls and small aquariums. These fish are very hardy but here's the issue. Your putting a creature that reaches 2 feet in length in an aquarium that is less than a foot long.

Now some people have this old wise tail going around that a fish will only reach the size of it's habitat....well....that's partially true and partially false. The smaller habitat will slow down their growth rate but their organs will continue to grow at the average rate while the body stays small thus compacting and eventually crushing all of the organs. It's a slow painful death.

So the real questing is: What size tank to I need to properly keep gold fish and that answer would be a minimum of 60 for 2 fish and ideally 135 gallons for a few more.

With a 5 gallon tank there are other fish you can keep though. Let me put together a list of fish that would be more suited to what you want:
only 1 group of the following:
1 male and 2-3 female fancy guppies
1 pair of rams
3 Lamprologus stappersii
4 tetras that only reach 1 inch
and any VERY small group of 1-2 inch fish (remember that must be the size they max out at in adult hood.
3-4 danios (zebra)
1 single male betta splendens or Siamese fighting fish

The following can be added as janitor fish (cleaners)
1 corydora (for uneaten food)
1-3 snails (for algae)

a 5 gallon tank is really quite small and has many limitations. The gold fish can live up to 30 years and some have lived up to 50.
I'd recommend getting a larger tank if you are truly interested in becoming an aquarist or just having an aquarium for your viewing pleasure.