The ancient Chinese recorded a comet which was visible between 9 March and 4 May in 5BC and that could have been the Star of Bethlehem. Oddly enough even though the Gospel of St Matthew says the star went before the wise men until it stood over where the young child was, it seems King Herod wasn't aware of the star.
Some think that Luke's reference to Quirinius was a mistake, and that he was referring to an earlier census which took place in 8BC, which means if Jesus was born in 5BC, his parents must have settled in Bethlehem for a few years until fleeing to Egypt to escape the slaughter of the innocents.
But that theory leads us to another problem. If Mary was pregnant when she and Joseph went to Bethlehem for the census in 8BC, and didn't give birth until 5BC, that still gives her a pretty long pregnancy. Not ten years as the other version would have it, but still three years. Whichever way it happened, there's definitely a chronological problem with this story.