I started with a 1 gal, got online here, went to a 2.5, and then started the 5 gal vs. ten gallon debate. Ultimately, I went with a ten gallon Aqueon kit, but substituted a sponge filter. I personally am MUCH happier with the ten than I think I would have been with the five. In my area, it seems all the lights, hoods, etc. available are for ten gallon, and I was worried if something broke that I wouldn't be able to easily replace it. I do a water change on Saturdays, and all is well.
I will add that, despite it being quite debated on here, I did decide in the beginning to start the tank with Tetra SafeStart (reading the bottle directions and online Tetra website directions and forum Q and A carefully) with five harlequin rasboras. It has mixed reviews on the forum, but it worked for me. I do have an API water test kit, and used it often in the process, and I kept my betta in his 2.5 until the ten gal was ready.
Just a few cents' worth...not everyone has room for a 10 gal, and I thought I didn't, either. But the more research I did, the more sense it made to go to it (easier to maintain water quality, etc.) I'm a newbie with a busy family, so I needed something easier. There do seem to be tons of people on here who are happy with their five gallons, though...It's great to review OFL's sticky on water changes to see what fits your lifestyle regarding tank size. My 2.5 gallon was working me to death, so the 10 really was a much better option for me. My betta stayed in his 2.5 while I did all the research and local purchasing/online ordering, but once it all got in, set up, and cycled, I think he's happier, too.
With a five gallon, your betta will be at double his current size, so I'm sure he will be happier! How about substituting a sponge filter for the kit you're looking into? They are relatively inexpensive and highly recommended here.