Sleep advice..

My girl is about the turn 5 months old, she has slept through on the odd occasion but generally she wakes between 3-5 am she rarely wakes up crying just babbling and chatting to herself, I usually give her a bottle and after that it doesn't take her long to go back to sleep but I'm not convinced she wakes for a feed as she's not crying for it .. I tried just leaving her to chat and hope that she'll get bored and fall asleep but she just gets louder and louder! 

Any advice on how to stop her waking would be gratefully received