Hi...I use a sponge filter in my 5.5 gallon betta tank. It's run by an air pump (Tetratec 12) and hooked up thru a gang valve (Penn Plax, I think) to lessen the air actually getting to the sponge filter. The sponge filter has a nice stream of bubbles coming up, that the betta likes to play in, but there is no current and the top of the water is almost perfectly still.
I think just about all HOB
filters would be too much for a betta in a 5.5 gallon tank. I have read that some people have a small Whisper or Aquaclear mini in their 5.5 gallon, but they have something other than a betta in the tank.
In my opinion, a sponge filter is all you need in a 5.5 gallon betta tank. The bettas do not create a huge bio-load. The sponge filter provides a place for the good bacteria, and my readings are always 0 (ammonia), 0 (nitrites), and 20 (nitrate). In my betta tanks, I don't think I need a HOB
to provide mechanical or chemical filtration. I do have a corner filter that I use carbon in occasionally (I take it in and out as needed.)
Here is the sponge filter I use:
It's rated for a 15 gallon tank, but I think it's ok in my 5.5 gallon.