My two puppies age 5 1/2 months & 6 months were also in that habit of 5am. I did it for a while, from about 4 month of age until 5 1/2 months (the older one's age) and then I got tired! They sleep in crates next to the bed at night. I started to ignore them 15 minutes at a time. First week I started, I wouldn't take them out until 5:15 am. I used a squirt bottle of water and everytime they started to whine I sprayed them. The second week it was 5:30 am. They now sleep until 7 am when the alarm goes off and I don't have to squirt them anymore. So all in all it took about 6 weeks to recondition their wake up time. The breeder where they came from used to get up at 5am and they were just in that habit. If your baby has everything she needs in her pen and you're not expecting her to hold her pee more than she's able to at this age, I would definitely more her to another room for sleeping until you can break this cycle. A tired Mommy & Daddy aren't any good to anyone!