Jesus was born, um, somewhere around this time

[Godscreated]

The Jesus Timeline (posted in the general religion section because Muslims have to account for it, too)

Jesus was born during the reign of Herod the Great

Matthew
2:1 Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king, behold, there came wise men from the east to Jerusalem,

Herod the Great died in 4 BCE, so Jesus would have to have been born before then.

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Jesus was also born during the administration of Gov Quirinius of Syra

Luke 2:2 (And this taxing was first made when Cyrenius was governor of Syria.)
...
2:5 To be taxed with Mary his espoused wife, being great with child.

Quirinius wasn't governor of Syria until 6 CE, so Jesus was born after that year.

So Jesus was born before 4 BCE and after 6 CE at the same time. Now that is a miracle.

Jesus started his ministry after his baptism by John the Baptist. JtB didn't start his ministry until 29 CE, during the 15th year of Tiberius.

Luke 3:1 Now in the fifteenth year of the reign of Tiberius Caesar, Pontius Pilate being governor of Judaea, and Herod being tetrarch of Galilee, and his brother Philip tetrarch of Ituraea and of the region of Trachonitis, and Lysanias the tetrarch of Abilene,
3:2 Annas and Caiaphas being the high priests, the word of God came unto John the son of Zacharias in the wilderness.

So Jesus didn't start his ministry until after 29 CE. Actually, JtB needed to start his ministry, become so renown as to be called the second coming of Elijah, p.o. Herod Antipas, get arrested, get thrown in prison, executed and then Jesus started his ministry. That would be a lot to happen in just one year.

Jesus was about 30 at his baptism

Luke 3:23 And Jesus himself began to be about thirty years of age,

So Matt's Jesus who was born circa 5 BCE (Herod died in April of 4 BCE) would have been "about 30" around 26 CE, three years before JtB even started his ministry, never mind all the other events. This is such a stretch that some apologists try to argue that "about 30" could mean 37 years old.

Additionally, Judea was a client state of Rome under the reign of King Herod the Great, so Luke's tax census wouldn't have happened even if we could somehow grant Quirinius an earlier governorship of Syria (an ad hoc that apologists often appeal to despite that we know where Quirinius was at the time and it wasn't Syria).

Luke's Jesus seems a little more plausible. The age of 30 fits with a birthday around 6 CE and it also fits with events of the arrest and execution of JtB, which based on Josephus' writings, would have been around the mid 30s CE. Where we run into problems is with the ministry and execution of Jesus.

Pontius Pilate, governor of Judea, was called back to Rome in 36 CE. This means the latest that Jesus could have been crucified would have been on Easter of that year. This would have only given him months, not years, to conduct his ministry.

The Gospel of John articulates that there were three Passovers over the course of Jesus' ministry and therefore 2-3 years. One needs a big shoe-horn to squeeze that in the months Luke's Jesus would have had.

John 2:13 And the Jews' passover was at hand, and Jesus went up to Jerusalem.
6:4 And the passover, a feast of the Jews, was nigh.
13:1 Now before the feast of the passover...

The devil's in the details, they say.

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Jesus was conceived in 3BC and Herod the Great died in 1BC according to all the manuscripts written before 1500AD. After this date there seems to be an error in copying to have given the 4BC date. The closer to the event the more reliable the data.