What difference does it make? They are multiples of five. Are they okay to him? I doubt that is so. He dislikes chunks of five. He was not prescribing semicolons. That would still bother him.
I think you might be missing the forest for the trees, here. It's not about five-word sentences; it's about the repetition making the paragraph as a whole monotonous and robotic - something you demonstrated very well in this very comment.
The OP primed you to read it robotically. I'll admit my sentences seem somewhat contrived though.
I was delighted when I first read the short, punchy, and somewhat dislocated clauses of The Stranger by Camus. Actually, a more pertinent example is the first page or so of Molloy by Samuel Beckett. Maybe the reader is supposed to be bored; I find it refreshing.
