At night you just let them sleep for however long they want.
5:20am counts as a night time feed, so you would feed and put back to sleep and then start the day when ever that is (7/7:30/8,etc.)
We always woke dd up at 7am to start her day, if she wasn't already up, to help her body's internal clock.
But, some lo's days start at 8am, so it's all dependent on what works best for your baby and your family.