The 5 Epagomenal Days

The 5 Epagomenal Days (6 during leap years) were inserted into the Egyptian Calendar which had been 360 days long. These days were reserved as birthdays for the gods. The first, third, and fifth of these days were considered unlucky by the Egyptians.

The legend behind the days holds the Nut had been forbidden to have children on any day of the year by her husband Geb. Thoth, upon hearing this, gambled with the moon-god for a fraction of his light. Thoth won and he created the additional 5 days for Nut so she could bear children on these days "not of the year."
They are as follows:

• July 27 - 1st Epagomenal Day - Birthday of Osiris
• July 28 - 2nd Epagomenal Day - Birthday of Horus
• July 29 - 3rd Epagomenal Day - Birthday of Set
• July 30 - 4th Epagomenal Day - Birthday of Isis
• July 31 - 5th Epagomenal Day - Birthday of Nephthys

Note:

These dates come from Traci de Regulla in The Mysteries of Isis. She took her dating from Dr. Robert Brier's Ancient Egyptian Magic. There is a great deal of dispute when it comes to calculating the dates of Egyptian festivals due to problems in their calendar system (it was only 360 days for some period of time).