Most my boys seem happy with about 4 gallons of volume.
Generally preparing the filter shipped with the tank for Betta use involves intake protection AND outflow retardation. Some filters like the larger Tetra are designed to make ANY amount of flow jet into the tank.
The preferred intake filter sponge for half inch intake pipe filters (5g 10g, marineland 2,3,5,6g, Aqua-Tech and Aqueon to 30g) is a Fluval Edge's intake pre-filter sponge but you can get away with a cut section of non-treated scrubby pad and a baby sock twist-tied onto the intake. Its usually good to put some kind of protection over the intake because betta like to perch on things, even just the sock will keep them from being wrapped around the intake area.
Out-flow on these filters you can usually cut a block sponge from wally world to fit the "chute" of the filter return shelf. My preference is to use nylon bolt and nut through a hole in the return chute to stick the baffle on with. Most people are fine with rubber bands and I have seen fishing line (if you're good with knots) and you can also use a nylon stocking that has the sponge in the bottom then gets hung over the filter. Some of the more ornate baffles involve cutting water bottles and sometimes superglue.
To be honest your best long term solution for a happy boy is a "H-0" from http://www.jehmco.com/html/hydro-sponge_filters.html
Sponge filters need air stones, tubing and an air pump. All of which come to about $13.00 at Walmart. The sponge will last most of a decade and doesn't need carbon or fiddly bits. If you order online a "Hawkeye" brand air-pump is the preferable one for a H-0. Hawkeyes can be adjusted by unscrewing the top cap a little at a time.
An alternate to that is a little Lee's/Tom's sponge filter. They're small yellow things and need the same air pump but don't need a stone.
Another option is an Aquaclear20 filter (petco should have it) run at its lowest flow setting. Don't use the carbon bag and don't bother replacing the ceramic nodes. (The Aquaclear20 will still need a baby sock over the intake.)
It depends on whether the $15 to $25 these methods costs is worth it to you vs the time it takes to baffle the filter you have.
If the 5g you bought is an Aqua-Tech there's one more trick you can do.
The design series of that filter was originally made so that a small lift to the intake pipe (upwards inside the filter) could reduce the overall flow by allowing recirculation around the impeller - thus the slots in the sides of the impeller housing's intake funnel. You can tie a rubber band around the intake pipe up where it rests and get some rise out of it. This isn't a highly reliable method and it can be pretty random with water level changes due to evaporation but it DOES work for the Aqua-Tech brand filters (originally Regent, now a Marineland bargain product)
If the tank has a Tetra Whisper internal filter there's a much simpler solution. The newer Whisper 5 seem to be coming out with adjustable pumps attached. The older ones can be slowed way down with a couple layers of nylon stocking over the bottom intake grill.
Aqueon filters can be slowed down much the same way as well as by inserting a piece of cut down vinyl hose into the top of the intake tube to create a flow restriction. Make sure any blockage you put in the intake pipe is wedged in snugly, you risk jamming the impeller.