Based upon the below, I believe the Savior was likely born on December 23, 5 BC. There is certainly not enough evidence to prove this scientifically, but if one is going to go out on a limb, consider going all the way out.

December 25th or January 6th

Andrew McGowan’s article  “How December 25 Became Christmas” (originally appeared in Bible Review, December 2002) notes the following:

By the fourth century, however, we find references to two dates that were widely recognized—and now also celebrated—as Jesus’ birthday: December 25 in the western Roman Empire and January 6 in the East (especially in Egypt and Asia Minor). The modern Armenian church continues to celebrate Christmas on January 6; for most Christians, however, December 25 would prevail, while January 6 eventually came to be known as the Feast of the Epiphany, commemorating the arrival of the magi in Bethlehem. The period between became the holiday season later known as the 12 days of Christmas.

“Dating the Birth of Jesus Christ” by  Jeffrey R. Chadwick in BYU Studies is a persuasive paper discussing at length the year of the Savior’s birth.  In it he reviews LDS authorities opinions on the date, noting that both J. Ruben Clark and Bruce R. McConkie concluded that Savior was born around 4 BC.  Going far beyond simply relying upon those authorities using many forms of evidence, he concludes it was likely late December 5 BC.

…the beginning of winter in 5 BC, specifically the month we know as December, remains as the only proposed window of time in which the birth of Jesus in Bethlehem can logically have occurred…

…the traditional date of Christmas, December 25, falls within the window of time in which it would appear that Jesus must have been born. It is just as possible that Jesus was born on the calendar date we call December 25 as on any other date in the few weeks preceding it or the week following it. But this study in no way concludes that December 25 was actually the birth date of Jesus. While people may always see things differently, the totality of the evidence presented above allows only one conclusion: that his birth occurred within those December weeks that we now commonly refer to as the Christmas season.  (“Dating the Birth of Jesus Christ” by  Jeffrey R. Chadwick in BYU Studies 49:4, page 25-26)

McGowan’s article refutes the common idea that early Christian leaders adopted a pagan holiday as the date, noting that evidence of celebration of December 25 or January 6 predates general acceptance of Christianity in the Roman Empire, when Christians continued to strongly differentiate their beliefs from paganism.  He then concludes with the following:

In the East, too, the dates of Jesus’ conception and death were linked. But instead of working from the 14th of Nisan in the Hebrew calendar, the easterners used the 14th of the first spring month (Artemisios) in their local Greek calendar—April 6 to us. April 6 is, of course, exactly nine months before January 6—the eastern date for Christmas. In the East, too, we have evidence that April was associated with Jesus’ conception and crucifixion….Even today, the Armenian Church celebrates the Annunciation in early April (on the 7th, not the 6th) and Christmas on January 6.

Thus, we have Christians in two parts of the world calculating Jesus’ birth on the basis that his death and conception took place on the same day (March 25 or April 6) and coming up with two close but different results (December 25 and January 6)….

The notion that creation and redemption should occur at the same time of year is also reflected in ancient Jewish tradition, recorded in the Talmud. The Babylonian Talmud preserves a dispute between two early-second-century C.E. rabbis who share this view, but disagree on the date: Rabbi Eliezer states: “In Nisan the world was created; in Nisan the Patriarchs were born; on Passover Isaac was born … and in Nisan they [our ancestors] will be redeemed in time to come.” (The other rabbi, Joshua, dates these same events to the following month, Tishri.)  Thus, the dates of Christmas and Epiphany may well have resulted from Christian theological reflection on such chronologies: Jesus would have been conceived on the same date he died, and born nine months later

April 6th as a death date for the Savior is interesting in that Chadwick, in a separate article, proposes it as the correct date for the Crucifixion

The numerous avenues of inquiry explored in this study together demonstrate that Jesus died on Thursday, April 6 (Julian), AD 30, which was the 14th day of Nisan in the Judean calendar, the day of the preparation of the Passover.   (“Dating the Death of Jesus Christ,” Jeffrey R. Chadwick, BYU Studies 54:4, page 188-190)

Returning to McGowan, he gives more details on the history of the December 25th date, nine months before March 25th.

Around 200 C.E. Tertullian of Carthage reported the calculation that the 14th of Nisan (the day of the crucifixion according to the Gospel of John) in the year Jesus died was equivalent to March 25 in the Roman (solar) calendar. March 25 is, of course, nine months before December 25…(“How December 25 Became Christmas”)

Although not stated directly, it seems possible to me that the difference between the 14th of Nisan being on April 6th or on March 25th is partially because the Jewish Calendar was a lunar calendar, which means dates changed relative to the Julian (solar) calendar.   Thus the March 25th date is tied to the year AD 33, (Christ supposedly having been born in the year 1 BC), whereas the April 6th date is the proper date in 30 AD, the year Chadwick proposes, if he was born in 5 BC.  It could also be partially due to better Jewish to Julian conversion abilities from the originally calculated dates in 200 C.E.

Thus,

• If Chadwick’s date of death of April 6, AD 30 is correct for the Savior’s death,
• And the tradition that the Savior died on and was conceived on the same day is correct,
• And the Savior’s gestation was a full nine months,
• Then the Savior’s birth would have been on January 6th.
• A birthdate of December 25th means either the date of his death is not April 6th, or the idea of conception and death dates being the same is incorrect, or his gestations was less than 9 months.

From here we depart from things that can be assessed scientifically.

Another Possible Date:  The Night of the Winter Solstice

Russel M. Nelson in visiting the Lewisville, Texas Stake in December of 2011 spoke to the adults of the birth of the Savior.  Within his talk, he had us consider, given the speed of light, how long before the birth of the Savior whatever event it was that created a new star had to have happened, to allow the light to arrive on earth on that specific night.

He then paused and said, “There is great order in the universe.”

In my own life, I have noted innumerable times when some event happened very near if not exactly on some personally significant date; a new assignment coinciding with the start date of a similar new assignment by 10 or 20 years or other similar coincidence.

Given this I can believe there is significance to the dates involved.  In that vain, it seems possible that the Savior’s birth could be tied directly to the Winter Solstice in the northern hemisphere, the day of the shortest amount of sunlight, and the longest night. The Winter Solstice occurs yearly on either December 21st or 22nd. Chadwick acknowledges this possible connection in a footnote to his article.

The third consideration seems to have been Christian recollection of earlier Jewish traditions that identified the coming of Messiah with the symbol of the rising sun. The book of Malachi foretold the coming of Messiah with this phrase: “unto you that fear my name shall the Sun of righteousness arise with healing in his wings” (Malachi 4:2). The Hebrew term in this passage of Malachi reads shemesh tzedakah, literally “the righteous sun.” The symbolic connection of the rising sun to the coming of Messiah was also mentioned by Zacharias, the father of John the Baptist, when he prophesied that John would prepare the way for the Anointed One’s arrival “to give knowledge of salvation unto his people by the remission of their sins, through the tender mercy of our God; whereby the dayspring from on high hath visited us, to give light to them that sit in darkness and in the shadow of death, to guide our feet into the way of peace” (Luke 1:77–79). The word “dayspring” in the King James Version of Luke 1 is simply another term for the rising sun—the Greek term is anatoli, literally “sunrise.” Jews at the time of the New Testament, including Jesus’s disciples, identified Messiah’s coming with the symbol of the rising sun. And this symbol seems to have been remembered into the fourth century by gentile Christian bishops, who saw no problem in using the Sol Invictus festival, which honored the sun, as a day to commemorate the birth of the “Sun of righteousness.”  (ibid. Page 38)

He notes that is possible that December 25th is the day as the lengthening of the day is perhaps not noticeable to the ancients until a day or two after the solstice.  Is it possible that those calculating his birth many centuries after his death were led to the wrong but close date by improper conversion of the calendar? Or perhaps they sensed some connection to the solstice, but did not know the actual date, and instead simply got close?

Richard Fitzpatrick, Professor & Research Scientist, Department of Physics & Institute for Fusion Studies, University of Texas at Austin, calculated for me that “the winter solstice in the year 5 BC occurred on December 22.”  (Private correspondence, January 29th, 2019).

I can also imagine the Savior of the World, the “bright and morning star” (Rev. 22:16) would have ushered into the world a period of increasing light from the long dark night that had enveloped it before his birth.  It is possible that the Savior’s conception may well have been on April 6, 5 BC, but that his gestation was something shorter than a total of 9 months.  How appropriate for him, in “descending below all things” (D&C 88:6) to have also suffered from a (slightly) premature birth.

Based upon this, I think his birth was likely in the early morning of December 23, 5 BC.

And Joseph Smith, the great latter-day revelator of Jesus Christ, perhaps was born on the same day of the year, December 23rd, 1805.  I believe there is indeed great order in the universe, and not all of it can be proven scientifically, today.