Varying contemporary sources indicate that Herod died in spring of 4 BC. So of course Jesus must have been born before that. It was unlikely to have been during winter (and the details don't require it), so the fall of 5 BC is more applicable.
While doing a study of the events depicted in Acts (I was interested in knowing when certain events took place, to track the growth of the Church), the estimated year of Jesus' death comes to be about 30 AD. Based on the gospel of John, his time of preaching started a few years before that (Jesus goes to Jerusalem for Passover multiple times over the course of John's narrative), bringing us to roughly 26-28 AD. In Luke, Jesus was 'about 30 years' when he began preaching. So... cut back 'about 30 years' from 26-28 AD, and we get a time frame of about 5-3 BC. Since 4 and 3 BC don't work... 5 BC is more applicable.