According to an authentic narration in relation to the birth of Hazrat Uthman (ra), it is mentioned that he was born in Mecca six years after the Aam al-Fil [Year of the Elephant]. It has also been stated that he was born in Ta‘if. He was approximately five years younger than the Holy Prophet (sa).
(Ali Muhammad al-Salabi, Sirat Amir al-Momineen Uthman (ra) bin Affan Shakhsiyyatuhu wa Asruh, Ch. 1 [Beirut, Lebanon: Dar al-Ma‘rifah, 2006] p. 16)