How does Kino kill a man in chapter 5 of The Pearl?
Kino killed a man with a knife in a fight for the pearl.
The incident you are describing is when Kino killed the man with the knife. Kino is a target because of the pearl. He defends himself with a knife. He describes the incident to his brother, Juan Tomás.
"I was attacked in the dark," said Kino. "And in the fight I have killed a man."
"Who?" asked Juan Tomás quickly.
"I do not know. It is all darkness - all darkness and shape of darkness." (Ch. 5)
The incident is actually more complicated than this. Juana tried to take the pearl and throw it back in the ocean, because she thinks it is bad luck. Kino tried to stop her, attacking her and beating her. He was angry, both because she would betray him and in fear and blind terror of losing the pearl. Upon returning, with the pearl, he is attacked by the unknown assailant that he stabs.
When Juana realized that her husband killed a man, she believed that the whole thing was because of the pearl and its bad luck. She wakes Kino up and tries to explain to him that they need to leave.
“Can you understand? You have killed a man. We must go away. They will come for us, can you understand? We must be gone before the daylight comes." (Ch. 5)
It is worth noting that when she finds Kino unconscious and he wakes up disoriented he is not concerned with the body next to him, but instead with where the pearl is. It has consumed his entire consciousness. Juana probably thought her husband was dead when she first saw him lying there next to the dead man. All she saw at first was “two dark figures lying in the path.” She definitely knew that the pearl was the trouble over which her husband killed the man.
Superstition aside, Juana is right about one thing. The pearl is trouble. This item they thought would make them rich causes them to lose everything. Because of it, their baby dies, and their lives will never be the same.