If you want a helpful introduction to the issue of when Jesus was born (and when other events in his life happened), check out Paul Maier’s article, “The Date of the Nativity and the Chronology of Jesus’ Life,” originally published in Chronos, Kairos, Christos: Nativity and Chronological Studies presented to Jack Finegan, ed. J. Vardaman (Winona Lake, IN: Eisenbrauns, 1989), 113-130.Maier's article [available at the link as a pdf] begins:
In 1968 I published an article that offered fresh evidence in support of Friday, 3 April A.D. 33, as the date of the Crucifixion. Since then, much attention has focused on the other terminus of Jesus' life in response to recent recalculations of dates for the death of Herod the Great and the birth of Christ. Although a precise date, as in the case of the Crucifixion, still seems unattainable for the Nativity, some further refinement within the usual range of 7 to 4 B.C. is possible, which would suggest late 5 B.C. as the most probable time for the first Christmas.