Chapter 5 describes the aftermath of the accident in which Finny falls out of the tree after Gene jostles it.
This chapter dispels Gene's paranoid idea, rising from Gene's own insecurity and sense of inadequacy, that Finny is just pretending to be his friend to divert him from his academic studies and thus win an imagined competition between them. We see in this chapter that even after the accident, Finny considers Gene his best friend. One quote that expresses this is when Dr. Stanpole says to Gene,
He wanted especially to see you. You were the one person he asked for.
Gene, still suspicious and paranoid, fears that Finny only wants to see him to accuse him of jostling the tree; in fact, Finny wishes to see him out of friendship. Finny is willing to rearrange what happened in his mind to protect his friendship. He tells Gene he had a feeling Gene jostled the branch but then backs away from any accusation:
"It was a crazy idea, I must have been delirious. So I just have to forget it. I just fell,” he turned away to grope for something among the pillows, “that’s all.” Then he glanced back at me, "I'm sorry about that feeling I had."
Hearing this, Gene realizes what a true friend Finny is:
And I thought we were competitors! It was so ludicrous I wanted to cry.
Gene shows he feels friendship for Finny in this chapter when he puts on his clothes and, for a moment, imagines he has become Finny, revealing his admiration for his friend:
I had no idea why this gave me such intense relief, but it seemed, standing there in Finny’s triumphant shirt, that I would never stumble through the confusions of my own character again.
Gene visits Finny in his home in this chapter and tries to tell him the truth:
I deliberately jounced the limb so you would fall off.
But then he realizes that if he is a true friend to Finny, he must promote the myth that it was an accident:
It struck me then that I was injuring him again. It occurred to me that this could be an even deeper injury than what I had done before. I would have to back out of it, I would have to disown it.
Finny and Gene remain best friends because Finny is the kind of person who refuses to see the dark side of a friend. He believes in Gene's worth in a way Gene himself cannot. Gene, through Finny's response to the accident, is reassured that Finny did truly like him all along and wasn't trying to sabotage him, which helps cement their friendship.