Hello welcome to the forum! Afraid have a little bit of bad news hon. A 5gallon is not big enough for those three fish. The goldfish themselves will need a much much larger tank whic does surprise most people. The reason being that these guys grow quite large and are messy. The whole "a fish will grow to the size of the tank " thing is rubbish, the physical size of the fish will grow to the tank it is in but the organs inside continue to grow which isnt healthy for the fish and will result in premature death. Local fish stores really should be shot for giving out bad info as a friend of mine has a £12.99 set up with shubunkin (she had two) one died instantly, the other continues to live but mopes around, yet my friend refuses my help. It is very sad in deed.
Also fighter fish do not always like other tankmates, some will kill on sight, others may have a more gentle temperament. I would be very careful with this combination in such a small tank.
Did you cycle the tank and filter as noticed got the betta a week ago and now added goldfish, his behaviour could also be a sign of ammonia/nitrites build up which also kills them or makes them ill. The goldfish being messy may also be too much for the filter in that space as well. Have you a test kit, can you get the water parameters? Also what do you feed the fighter as flake food is not best for them.
lastly there arent much in the way of decorations in there, fighters are curious and rather intelligent fish, he may not feel the need to explore, espcially with the other two fish taking up most the space.
Sorry to be such a negative nancy but you may end up with dead fish on your hands due to a number of ways if we do not get this sorted..My main suggestion would be to take the shubunkins back, as that tank is far to small as it is. Get a couple of cheap silk or live plants (plastic will rip the fighters fins) and there are a couple of tankmates out there that can add if wish to make more interesting. Most people on here recommend 3-5g for a fighter fish (betta) but there are some cool things to add. For instance I have a aquatic African Dwarf Frog in mine and it is interesting watching!
Just off to find a small list of occupants
Cant find the link right now, will keep looking, one thing also to add that the shubunkins are coldwater and the fighter is tropical and unless live in a warm area should really have a heater, especially during the winter
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