There are five fasts each year because of sad things that happened to the Yidden:
1) Tzom Gedaliah (Gimmel Tishrei) — when Gedaliah was killed. He was the governor of the Yidden, and they hoped he would help them live in Eretz Yisroel. When he was killed, the Yidden realized they were REALLY in Golus.
2) Asara B’Teves — When Nevuchadnetzar blocked anyone from going out or coming into Yerushalayim.
3) Shiva-Asar B’Tammuz — 5 sad things happened: The luchos were broken, the Yidden couldn’t bring korbanos anymore (in the first Beis Hamikdash), the walls of Yerushalayim were broken (in the time of the Second Beis Hamikdash), Apostomos the rasha burned a Torah, and he also put an idol in the (second) Beis Hamikdash.
4) Tisha B’Av — 5 sad things happened: The Yidden in the Midbar were told they wouldn’t get to go into Eretz Yisroel, the Beis Hamikdash was destroyed (both), a city called Beitar was captured and everyone was killed (including Bar Kochva, who many Chachomim said could be Moshiach), and the rasha Tineius Rufus plowed the ground of the Beis Hamikdash (this is something the Navi said would happen).
The Yidden also took the minhag of fasting one more fast:
5) Taanis Esther (Yud-Gimmel Adar) — we fast Erev Purim to remember how all of the Yidden fasted in the time of Haman.