The advantages of having a hang-on-back (HOB) filter are worth considering. The media is away from the fish and gravel and can be kept alive without having to worry about over-cleaning the gravel. When you are relying on your gravel to keep the nitrifyers alive, there is a delicate balance waiting to be upset by you or the fish. UGF's are effective and work fine for plenty of situations. But having a box filter of any kind almost guarantees your bacteria will survive, unless you medicate the tank or something.
You said something which indicates you may not understand the nitrogen cycle. You said that, since fish have stayed in the tank, the tank is still cycled. The truth is, an aquarium can be cycled with pure ammonia and no fish. The fish's nitrogenous wastes are what feed your beneficial bacteria, like the pure ammonia would if you were cycling from scratch. My point is, your tank is not cycled if you test positive for any ammonia. To leave the fish in that water is to poison them. Their gills are burning, their slime coats are peeling. Get them out of there or get that water out of there. Either one may save some fish. After this, though, none of those fish will live normal lives. Ammonia poisoning usually scars the gills, making breathing difficult.
I don't mean to scare you, I just want to make it clear that the fish cannot be in that water for another moment.
You say nitrAtes are 5. That is a little lower than normal, except in a heavily planted tank. As your Ammonia turns into nitrIte, then nitrAte, those nitrAte levels will rise sharply. That's where routine water changes come in. 30% weekly is the standard, but it varies by the metabolism of your tank.