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Though I have read Ezra and Nehemiah in the past, I had not gone through the lists to compare the numbers they provide. Re-reading through and seeing how they differ in certain counts made me have the same question of wondering why they differ.
You mentioned not finding sufficient evidence with the common answers such as it being caused by scribal errors or because they were written in different times, so I will do my best to provide a more solidified response to this apparent contradiction.
After researching this topic I’ve found a few potential solutions to this. However, I want to provide the simplest one because this is what I believe makes the most sense and is the most sufficient. Nehemiah 7:5 reads,
“5 Then my God put it into my heart to assemble the nobles and the officials and the people to be enrolled by genealogy. And I found the book of the genealogy of those who came up at the first, and I found written in it:”
Nehemiah is not claiming that God spoke these numbers to him, he’s stating that these are the numbers from the book of genealogy he found. God’s Word accurately gives us the numbers from the documents Nehemiah found, there is no requirement that they match up with the correct numbers in Ezra 2.
This is not the only time in Scripture that an author cites extra biblical sources in their writing. In Jude 9-15 Jude references the Book of Enoch, a set of several pseudepigraphal works that attribute themselves to Enoch, the great-grandfather of Noah (Genesis 5:18). The Book of Enoch is not canon for Scripture, nor is it even included in the Apocrypha. Another time is when Paul references pagan poets/authors (likely Epimenides of Crete in the first quotation, Aratus’s poem “Phainomena” in the second) in Acts 17:27-29.
In both cases, Jude and Paul are not attributing their sources to being divinely inspired writings, but they do include references to them to pull meaning from and use it in a Christian manner. Similarly, Nehemiah’s account is simply using historical documentation at the time to pull information from about the number of those who returned from Babylon to Jerusalem during the time of Ezra and Nehemiah, not claiming that God directly gave him these exact numbers.
Also, we'd love to help out with any apparent contradictions you have questions about!
Additional reading:
The Census of Ezra 2 and Nehemiah 7 - Is the Bible Inerrant? *I recommend this one.
Resolving the Differences in the Return Lists (Ezra 2; Nehemiah 7:5-72)
Q&A: Ezra and Nehemiah discrepancies Thirdmill.
What are the Apocrypha / Deuterocanonical books? Got Questions.
What is the book of Enoch and should it be in the Bible? Got Questions.
Why Does the New Testament Cite Extrabiblical Sources? desiringGod.
What does it mean that something is extrabiblical / extra-biblical? Got Questions.
Does the New Testament quote extrabiblical writers? - Biblical Hermeneutics Stack Exchange This one is like a Reddit style page for theology, so make sure to discern anything you read with Scripture, just like with anything else.