Is this normal for a 5 day old newborn?

The first night home from the hospital she slept all through the night except at feedings which were about every three hours. These last two nights she has been awake from 12 at night until a little after 5 in the morning. Today we have tried to keep her awake as much as possible, but with a sleepy newborn its hard work. Is staying up so many hours at a time normal? I need some advice.