What age can baby have a binky?

My son is five days old and loves to suck. He is both breast fed (when he's patient) and formula fed from a bottle. Once he's done with his bottle he acts like he's still hungry because he doesn't give it time to kick in. He'll root for my breast but won't actually feed, he'll just have his mouth on it. I feel like getting him to sleep would be easier if he had a Binky to suck on after feeding but we heard he's too young. Anyone else have luck with this?