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

Sounds like baby is having fun discovering the use of her hands and mouth. Her hands are like toys to her as she discovers that they are actually part of her. Sucking on her fists could be a comforting mechanism or simply, your baby's way of discovering different sensations (her tiny fingers have many sensitive nerve endings).