@ 5 weeks they should be able to eat anything that a full grown betta can eat,only smaller. Get some Hikari bloodworms in the flat pack, break it in to tiny chunks than melt it in a cup with tank water, use an eye dropper to suck the melted bloodworms from the cup and squirt them in the tank a little bit at a time.
Same with frozen brine,except you shouldn't have to break them. They also go crazy for frozen daphnia at that age,or zooplankton.