With all due respect, your AC is giving you bad advice. Skip the 5th letter. In fact, you probably should have skipped the 4th. USNA mandates recs from a candidate's math and English teacher, your BGO and basically an endorsement of activities from a school official. Period. (You mentioned science teacher vs. English so I'm assuming your DS received dispensation from his Regional Director or other person in Admissions to substitute LORs; otherwise, he will be penalized for not following instructions.)
USNA accepts other letters with the unspoken huge caveat that they bring something new to the table. In most cases, this occurs because the candidate's only/primary ECA is outside of school, the candidate works to help support the family so has no ECAs and gets the LOR from the employer, or the recommender can comment about some aspect of a candidate's life that would not be known to the required recommenders.
Additional letters that don't meet that standard aren't going to be helpful and, in fact, will probably just annoy Admissions. Why? Two reasons. First, because they aren't adding anything new. We all know they're going to say some version of the following: I've known Johnnie (or Janie) since he was X years old. He is a wonderful young man. He's smart, athletic, a terrific leader, kind to animals, helps little old ladies cross the street, etc . He's wanted to attend USNA since he was old enough to understand the words and wants to be a Naval/Marine Corps officer more than anyone in the world. And so on. Not helpful. Seriously.
Second reason is that USNA receives about thousands of completed applications each year. If that number is 5,000, that means 15,000 REQUIRED LORs they have to read. If every one of those ~5000 candidates submitted 2-3 extra letters (that say nothing new), that means USNA has to read another 10,000-15,000 letters about how wonderful little Johnnie/Janie is.
Finally, almost the last thing USNA wants to read is a letter from you DS' high school classmate. (I can think of a couple rare examples where such a letter might be appropriate but only a couple). What is a 17-yr-old going to add to the equation?
Folks, LORs are not about volume; they're about content. If LORs from a candidate's teachers (most important) and BGO (important but less so b/c of the more limited time for knowing the candidate) aren't strong, the extra ones won't make any difference unless they are able to convey completely new information. And those situations are very rare.