John 4:16-19 (ESV):
16 Jesus said to her, “Go, call your husband, and come here.” 17 The woman answered him, “I have no husband.” Jesus said to her, “You are right in saying, ‘I have no husband’; 18 for you have had five husbands, and the one you now have is not your husband. What you have said is true.” 19 The woman said to him, “Sir, I perceive that you are a prophet.
How did Jesus obtain this information about her?
There are two matters here.
Jesus was a prophet as predicted in Deut 18:15, 18-20 and documented as fulfilled in Acts 3:21-23. This is confirmed numerous times in other places such as: Matt 13:57, 21:11, 46, Mark 6:4, Luke 4:24, 24:19, John 4:44, 6:14, etc. This is NOT to suggest that Jesus was merely a prophet, He was the divine Son of God, but during His incarnation as Messiah, he was, among other things, a prophet.
The prophets were given access to divine information that enabled them to understand things beyond the reach or human knowledge and wisdom. This enabled the prophets to do remarkable things such as write the prophecies of Messiah and the future (2 Peter 1:19-21), etc. Such divine knowledge permitted the ancient prophets to know things about the king; eg, Elisha telling his king about what the enemies were doing, 2 Kings 6:8-23.
Thus, it is immediately clear that if Jesus were Messiah and a prophet, Jesus had access to divine knowledge via the enlightenment of the Holy Spirit to do some remarkable things.
That is, Jesus knowledge about the woman's past (John 4:18) does not necessarily suggest omniscience of Jesus. It simply confirms what the woman said next (V19), "Sir, I perceive that you are a prophet!"
APPENDIX - Logical possibilities
The above analysis does not necessarily preclude the possibility that Jesus was omniscient. [Here, I should declare my bias and say that I believe Jesus was omniscient, as well as omnipotent and omnipresent, etc.] However, as explained in the previous question here >> Did the disciples believe that Jesus was omniscient? , during Jesus' incarnations, these privileges were voluntarily put aside (Phil 2:5-8) so that Jesus depended only on the same power and authority that any other person has.
However - If Jesus used His innate omniscience to know all the things only known to divine knowledge, then He would NOT have been a prophet during the incarnation. That is, the very fact that Jesus was called a prophet means that He used the the Holy Spirit as the source of divine knowledge rather than His own.
Luke 7:
36Then one of the Pharisees invited Jesus to eat with him, and He entered the Pharisee’s house and reclined at the table. 37When a sinful woman from that town learned that Jesus was dining there, she brought an alabaster jar of perfume. 38As she stood behind Him at His feet weeping, she began to wet His feet with her tears and wipe them with her hair. Then she kissed His feet and anointed them with the perfume.
39 When the Pharisee who had invited Jesus saw this, he said to himself, “If this man were a prophet, He would know who this is and what kind of woman is touching Him—for she is a sinner!”
The Pharisee expected that a prophet knew things supernaturally. The Samaritan woman thought the same in John 4:
18 for you have had five husbands, and the one you now have is not your husband. What you have said is true.” 19 The woman said to him, “Sir, I perceive that you are a prophet.
How did Jesus know that the Samaritan woman had had five husbands?
Being a prophet, Jesus received a special revelation about the Samaritan woman.