Answer: The sentence that correctly uses a semicolon is the last one: The author has written four other books; this is book five.
Step-by-step explanation: A semicolon is one of the many punctuation marks added to indicate that there is a pause in a sentence. Moreover, a semicolon is used to separate two independent clauses, that is to say it is used to join two clauses that can stand alone but are related to each other due to the ideas they present. In that way, the semicolon is correctly used in the last sentence ("The author has written four books; this is book five") because it joins two independent clauses closely related ("The author has written four books" and "This is book five").