okay... for starters neon tetras are the tastey crunchy morsels of the fish world! (okay they aren't crunchy that are squishy) - and put them with a betta and let's call it a buffet!
females are actually very aggressive if you don't give them the right set up. a nice grouping a 5 females is wonderful with lots of floating plants. that way they all get to make their own little territory.
so if you want 5 females in a 10 gallon (IMO way to small) then you need to not have anything else in there except perhaps a few cories to clean up the bottom of the tank.
as for barbs... barbs, in nature, live in pools of water which dry up in the summer... so there can be hundreds of barbs in a very small area of water... with no food. so they nip each others fins and scales to stay alive. so it's not that they are aggressive... if you keep them in a school then they don't bother anyone else in the tank... they'll just nibble on each other.
keeping the two together is a recipe for disaster. i would not recommend it at all.
personally a nice 77 gallon community tank is perfect for a group of female bettas... and one male. (the reason you don't keep less females together with a male is because he'll pester her to breed till she dies... so you need lots of females so he spends time pestering each one and gives each female a break!)
hope that helps.