Basically the more fish you stock, the more frequent you need to do the water changes, as those test kits will tell you as well. It's generally i gallon per inch of fish, so while in theory you could fit two betta to a 5g (as well as accounting for water displacement by substrate and decor) they would have far less room to move around in.
I personally wouldn't divide a 5g (rather fill it with plants and caves and maybe a snail as a tankmate for one betta). My 10g's divided (one betta didn't like so much space, it was wierd) with one betta to each side each with his own snail.
It's rough because bettas need to be separated (thus needing so much room for tanks), but space to move and clean water are the biggest issues for a happy fish. The less betta you stock, the lower your chances of severe ammonia levels you could miss in only a 24 hour period.
Also, also, depending on your pH (7+) ammonia becomes a lot mroe toxic to your fish, so that's another factor to keep in mind. If you have high pH levels, you definitely dont want to risk overstocking. Mine's 7.5-8.0, so as much as I'd love to fill my tanks....lol, definitely playing it safe.
Sorry if you knew some or all of this or if it's just being repeated, lol.
Also, filters are important for larger tank systems, so I'd advise them, but try to find ones that don't have too strong a current (can harm/stress the betta) or can easilly be muffled.