Again, that's all up to your personal preference. The size of the tank will be determined by how many you want to breed and how long you want to keep them. You can easily end up with too many tadpoles, and none of your tanks could permanently house them all. I reccommend using the 10g if you plan on just keeping them. If you want to breed them, you need larger tanks in order to house a number of them long term.
I don't do breeding with anything under 10g so I wouldn't advise using smaller tanks for major breeding projects. I'm sure you can, but often there simply isn't enough water volume for multiple specimens and enough maintenance done to keep small volumes of water stable. You can grow out fry and breed dwarf shrimp in smaller tanks but I wouldn't try to do a bunch of tadpoles in a 5g. You can, but I wouldn't.
Live cultures are not necessary but if you want you can use blackworms, whiteworms, bloodworms, gammarus scuds, daphnia magna, or green water and infusoria.
When I tried this, I fed the adults with frozen bloodworms, dried daphnia, and live scuds. I fed dried daphnia and green water with infusoria to the tadpoles.