I believe that Jesus was born on Nisan 1, 5 BCE. This corresponds to March 9/10 in the Julian calendar.

Now I want to give three reasons why Jesus was born on Nisan 1.

1. Because it is exactly the same day that God's presence filled the Tent of Meeting (Ex 40:2, Ex 40:34). This event foretold the incarnation of God (Jhn 1:14, the greek word "skenoo" literally means "to tent"). On the same day that God came to earth to live in a tent, God also came to earth to live in a human body. In the New Testament we can clearly see that the old Jewish feasts are fulfilled in Jesus. Some examples: Jesus was sacrificed on the cross on the same day that the Passover lamb was sacrificed, because he is the true Passover lamb, the 14th of Nisan; and Jesus was resurrected on the same day that the first fruits were celebrated, because he is the first to rise from the dead to eternal life, the 16th of Nisan. So it makes sense that Jesus was born on a special Jewish day.

2. Since Jesus is the true Passover lamb (Jhn 1:29), it makes sense that Jesus was born in the month of Nisan, a spring month, because according to the law the Passover lamb must be 1 year old (Ex 12:5). 1 year before the Passover is the month of Nisan. So Nisan is the month when the Passover lambs were born. The shepherds who watched over their flocks on the day of Jesus' birth (Lk 2:8) were probably the shepherds who prepared the Passover lambs.

3. Nisan 1 is the beginning of the new year (Ex 12:2). Jesus was born on the New Year because he is the beginning of the new creation (2Cor 5:17).