The 5th of Kislev is the yahrtzeit (anniversary of the death) of Rabbi "Shemuel Eliezer Eidel's (1555-1631), also known by the acronym "Maharsha". Rabbi Shmuel authored a widely used commentary on the Talmud and of its primary commentaries, Rashi and Tosfot.
In the first decades of the 5th century, Rav Ashi (died in 427 CE) and Ravina I (died in 421 CE) led a group of the Amoraim (Talmudic sages) in compiling the Babylonian Talmud, which involved collecting and editing the discussions, debates and rulings of hundreds of scholars and sages which had taken place in the more than 200 years since the compilation of the Mishnah by Rabbi Judah HaNasi in 189 CE. The last of these editors and compilers was Ravina II, who died on the 13th of Kislev of the Hebrew year 4235 (or 475 CE). After Ravina II, no further additions were make to the Talmud, with the exception of the minimal editing undertaken by the Rabbanan Savura'i (476-560). This date thus marks the point where the Talmud has been since "closed," and has since served as a book for referencing Torah law.
Rabbi Abraham Maimuni HaNagid (also called "Rabbi Avraham ben HaRambam") was the only son of Maimonides (the Talmudist, codifier of Jewish Law, philosopher, physician and statesmen, Rabbi Moshe ben Maimon, 1135-1204). He was born in 1185, Rabbi Abraham succeeded his father as the leader of the Jewish community in Fostat (old Cairo), Egypt, at the young age of 19. He wrote many responses and commentaries explaining and defending his father's writings and Halachic rulings. Rabbi Abraham died on the 18th of Kislev of the Hebrew year, 4998 (1237).
the son of Rabbi Israel Baal Shem Tov's daughter, Adel, and her husband, Rabbi Yechiel Ashkenazi. He was born in 1753 in Mezhibuz, the town from which his illustrious grandfather led the Chassidic Movement. He was one of the Rebbes (Chassidic masters) in the 3rd generation of Chassidism, and had thousands of followers.
Ezra, head of the Sanhedrin and the leader of the Jewish people at the time of the building of the Second Temple, made an address to a three-day assemblage of Jews in Jerusalem, telling them to adhere to the teachings of the Torah and to dissolve their interfaith marriages (this was from assimilation due to their 70-year exile in Babylonia).
The vessels, tapestries, wall sections and other components of the Mishkan (the portable sanctuary or "Tabernacle" which was built under Moses' direction to house the Divine Presence during the Israelites' journeys through the desert) were completed on the 25th of Kislev of the Hebrew year 2449 (1312 BCE). However, the Mishkan was not assembled until 3 months later, when, beginning on Adar 25 of that year, it was set up and taken down daily for a 7-day training period prior to its dedication on the 1st of Nisan. The Sages said that Kislev 25 was compensated 12 centuries later, when the Maccabees dedicated the Holy Temple on Kislev 25, 3622 (139 BCE).
It is said that the forty days and nights of rainfall which covered the face of earth with water in Noah's time ended on Kislev 27 of the Hebrew year 1656 (2105 BCE). The flood itself lasted a full year (According to Genesis 6-8).