Over the past few years I have noticed some confusion over whether the 5th or 6th January is Twelfth Night. I always think it's the 6th, but others think 5th. Apparently this confusion goes back a very long way. As the 12th-century writer Orm notes here, people often called Epiphany 'Twelfth Day', though it's really the 13th day after Christmas...
So. that's all clear now!