Why do many synagogues hold festivities on the fifth day of Chanukah?

 

The fifth day of Chanukah can never occur on a Shabbat. When Chanukah occurs on days that are even only potentially Shabbat days, the light of Chanukah combines with the light of Shabbat for a powerful illumination. So the fifth night, which can never be Shabbat, represents great darkness relative to the other nights. Thus, the fifth light of Chanukah has the unique task and power to illuminate and instill spirituality even in such a time of darkness.

Similarly, it is the duty of every Jew, wherever he may find himself, be it in Warsaw, England, the United States or Canada, to illuminate even the greatest darkness.

- from a talk of the Rebbe in 1929 while in Warsaw Poland.

[Note: This talk encompasses a story than spans 60 years and is available electronically. Click here if you would like the story]

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In Chabad circles this day is of special significance because the Alter Rebbe, Rabbi Shneur Zalman of Liadi, was released from his second imprisonment on the fifth day of Chanukah, in the year 5561. He was imprisoned because the government scholars thought that some of the topics accentuated and expanded in his Chassidic philosophy might cause insubordination to the government and refusal to engage in mundane matters, though they are necessary for the existence of the world. Upon articulately clarifying his teaching and dispelling their fears, he gained his release.