Here's how it works: The left hand ball (let's call it A) has momentum. When it hits the ball second from the left (let's call it B), then B exerts a force on A to stop it. That force must be acting to the left. By Newton's Third Law, an equal and opposite force from A must then act on B. I was brought up to call this a reaction force. The reaction force pushes B to the right but C applies a force on it to stop it moving. A reaction force from B onto C pushes C forwards. And so on until E stops D moving. The reaction force from D onto E has nothing to stop it. E has a resultant force on it and off it goes.
