Answer: December 25th, Christmas
Why:
The zodiac sign in between Sagittarius (centaur) and Aquarius (water-bearer) is Capricorn. The dates of Capricorn is December 21st to January 19th. The months are either December or January. The fifth times itself is 5x5 equals 25. December 25th is also the day after Christmas Eve giving it the right answer.
