public int numFives () {
    int result = 0;
    Node x = first;
    while (x != null) {
      if (x.item == 5) result = result + 1;
      x = x.next;
    }
    return result;
  }

For [5,11,5,5], the values of x (line 14) are

x==[5,11,5,5], result==0
  x==[11,5,5], result==1
     x==[5,5], result==1
       x==[5], result==2
        x==[], result==3 (x==null)

Try setting a breakpoint and running in the debugger, and tracing the execution of the code simultaneously.