http://revach.net/article.php?id=3233

Section: Moadim   Category: Around The Year
Should We Fast On 5 B'Teves Or 10 B'Teves?

The gemara says that there is a Machlokes between Rebbi Akiva and Rebbi Shimon Bar Yochai if the pasuk that says "Tzom Ha'Asiri"; the fast of the tenth month is referring to Asara B'Teves the day Nevuchadnezzar laid siege to Yerushalayim according to Rebbi Akiva or 5 B'Teves theday that the news of the Churban Bais HaMikdash reached the people of Bavel according to Rebbi Shimon Bar Yochai since the day of hearing bad news is considered like the day it happened.

The Tur says we only fast on the 10th and not the 5th. Strangely the Rif and the Rosh both don'teven mention anything about 5 B'Teves at all. Why is there no mention of the fast on the hearing of the bad news? Not even that a "Baal Nefesh" should be machmir and fast on that day.

Rav Shlomo HaKohen MiVilna suggests (Binyan Shlomo OC 2:45) suggests that there is no machlokes L'halacha between these two tanaim.  Everybody holds that today we fast only on the 10th. The reason is that the fast of the Fifth of Teves was only for those in Galus Bavel at the time of the Churban, who didn't witness the Churban. They fasted the day they heard about it. They didn't fast Tisha B'Av. Since we don't know where our ancestors were during that time we only fast the day of the Churban itself Tisha B'Av.

If so why does Rebbi Shimon Bar Yochai say that the pasuk that says Tzom HaAsiri means the 5 Teves? The gemara says that this is because it is mentioned after the fast of Tisha B'Av in an otherwise chronologically correct Pasuk so therefore it must be talking about the fast of 5 Teves which happened after the Churban and not 10 Teves, which happened before.