The plants will help a lot, but make sure you keep up with the water changes. I dont think one of those small HOB whispers, or similar wouls make enough noise to keep someone awake though.
Azoo makes a little filter that is silent. I have one on my 2.5 gallon by my bed and it is great. It also is very cheap. It will run you about 7 bucks from www.drsfostersmith.com
Just so you know--it's kind of a pain in the a** doing constant water changes in a 5 gallon. Also, even with plants, you'll likely need something to move the water around so it doesn't get too stagnant in there. Having no filter can sometimes lead to a lot of particles floating around in the tank, the result being water that looks a bit cloudy.
I have seen betta tanks with no filter, but they were usually small 1-2 gallon jars where the person was changing out 50-100% of the water on a daily or bi-weekly basis.
Let us know if your plan works though. I'd love to ditch my filter for silence.
honestly, the tiny bit of noise the filter makes is white noise, which i find very comforting when trying to go to sleep. just make sure you have the water level high enough that it covers the filter outlet so you don't get the water trickle sound and it really shouldn't be a problem. i can't hear anything from my 2 whispers on my 20g.
I have bought 2 Aquaclear Minis for my tanks so far and returned both due to noise. Maybe I'm just unlucky, but these filters were not quiet enough for the next room never mind the room I sleep in!
Another note--you've got less than 1 watt per gallon of lighting on your tank, which will limit your plant choices--you'll need to stick to very low/ low light plant choices.