In New Testament times there were 7 festivals, or feasts in number. They were:
New Year and Yom Kippur
Lights or Dedication
The first five listed here were prescribed by the Mosaic law and the last two were post-exilic in origin.
In the Old Testament Leviticus 23 reveals seven "appointed times" set apart by the Lord as festivals or feasts unto Him. There were not feasts as we think of feasts today, but were holy times of sacrifice and worship unto the Lord. The feasts were:
The first four actually relate to the Passover, and the following three were all observed during the month of Tishri, the holy seventh month in the Fall.
The Jewish Calendar in Ancient Hebrew History
Bible History Online