Here is the definition of member.

      member(M, [M|X]).
      member(M, [X|T]) :- member(M, T).

The proof tree is below. A node contains a list of goal atoms, which you think of as a todo list. You always work on the first goal in the list. The top node has two children because there are two ways to solve goal member(X,[3,4,5]), not because there are two goals in the list.

The graphics is not beautiful, but this should do. The following tree shows all of the branches, even failed ones. The left-hand branch uses the first axiom and the right-hand branch uses the second axiom.

             member(X,[3,4,5]), member(X,[4])
            /                               \
            | X = 3                      member(X,[4,5]), member(X,[4])
            |                           /                              \
        member(3,[4])                   | X = 4
       /             \                  |
     fail      member(3,[])             |
              /            \            |
            fail          fail     member(4,[4])
                                  /             \
                               success