Baby getting up way too early

My almost 5 mo old lately has been getting up at 4 am and just stays awake in her crib making noises, sometimes by 5 am she's back asleep but after 5 am I get her change and feed her. My question is, are any other babies doing this? She's a grid sleeper we start bedtime process at 745 and she's in bed by 8 or 830. And sleeps till this time. What should I do? Get her and feed her right away? Leave her in the crib? What have you been doing. Of course I don't engage too much during the time shes up so she knows it too early. I'm exaut6as I do till go to work till 8amish bit up since 4. Heeelllppp