My 5 month old waves her hands back and forth in front of her face and likes to sucks on her fist. Why?

It is probably like what the rest have mentioned, your little one is experimenting and being fascinated by her hands. For babies, they learn about different parts of their bodies as they develop. Waving, clenching and releasing, trying to grab things etc are just part of the process of their motor skills development. Sucking on her fist is simply just a self-comforting behavior. You need not be worried about this. :)