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In many Western ecclesiastical traditions, Christmas Day is considered the "First Day of Christmas" and the Twelve Days are 25 December – 5 January, inclusive, making Twelfth Night on 5 January, which is Epiphany Eve.[1] In some customs, the Twelve Days of Christmas are counted from sundown on the evening of 25 December until the morning of 6 January, meaning that the Twelfth Night falls on the evening 5 January and the Twelfth Day falls on 6 January. However, in some church traditions only full days are counted, so that 5 January is counted as the Eleventh Day, 6 January as the Twelfth Day, and the evening of 6 January is counted as the Twelfth Night.[7] In these traditions, Twelfth Night is the same as Epiphany.[8] However, some such as the Church of England consider Twelfth Night to be the eve of the Twelfth Day (in the same way that Christmas Eve comes before Christmas), and thus consider Twelfth Night to be on 5 January[9] The difficulty may come from the use of the words "eve" which is defined as "the day or evening before an event", however, especially in antiquated usage could be used to simply mean "evening".[10]
Bruce Forbes writes: In 567 the Council of Tours proclaimed that the entire period between Christmas and Epiphany should be considered part of the celebration, creating what became known as the twelve days of Christmas, or what the English called Christmastide. On the last of the twelve days, called Twelfth Night, various cultures developed a wide range of additional special festivities. The variation extends even to the issue of how to count the days. If Christmas Day is the first of the twelve days, then Twelfth Night would be on January 5, the eve of Epiphany. If December 26, the day after Christmas, is the first day, then Twelfth Night falls on January 6, the evening of Epiphany itself.[11]
https://en.wikipedia.org/wiki/Twelfth_Night_(holiday)
http://www.holidays-and-observances.com/january-5.html