Here's another question: Can I just use filtered water in the tank and not use the Aqua Safe conditioner?
It depends. As someone here mentioned, keeping a small tank properly balanced is actually a lot more work.
I've had a 90 gallon for 10 years, with loads of live plants and the thing just ran itself. I moved twice in that time, and getting the sediment built up again took about 6 months. Loads of snails help, and a rascally skunk loach to keep 'em in check worked beautifully. (The loach would pile up the snail carcasses in one spot, like a bone pyramid, it was pretty funny).
For your size I'd recommend:
Only swap out 1/3 of the water per change is important.
Keep some porous rock material in it if you can (lava rock), whatever size you can accommodate in your tank. The bacteria love living in it.
When you clean your filter, depending on what it is, you may have to re-add conditioner (which I take it you mean the bacteria solution). If your filter has a block of foam, that's where most of the bacteria live (hence the recommendation for the porous rock).
You can tell if you have enough bacteria in the tank by monitoring the ammonia levels. High ammonia, too few bacterium. If you have enough bacteria, they convert ammonia to nitrites which end up as nitrates. Too much nitrate, the fish aren't happy and you likely get algae blooms (lots if the tank gets any direct sunlight). (Not much room in a 5 gallon to plant much, which would help with the nitrates).
Another good rule of thumb is one gallon per one inch of fish, although goldfish are big in comparison to tetras, so a one inch goldfish is like two tetras.
Good luck, enjoy.