Here's why:
* Internal evidence: The book itself gives clues about the time of writing. For example, Nehemiah 2:1 states that Nehemiah was appointed governor in the 20th year of King Artaxerxes I, which is generally accepted to be 445 BCE.
* External evidence: Historical records and archaeological findings support the idea that the events described in Nehemiah occurred around the middle of the 5th century BCE.
It's important to note that scholars are not in complete agreement on the exact date of writing. Some argue for a slightly earlier or later date, but the consensus points to the period mentioned above.