Step 1: Understand the given question and make a note of the all possible outcomes.

            NOTE: A die is thrown twice.  

                        So, Total number of event n(T) = 6 * 6 = 36

             Let us consider an event A of getting number 5 on at least one dice

              Events of getting 5 are n(F)= {(5,1),( 5,2),( 5,3),( 5,4),( 5,5),( 5,6),(1,5),(2,5),(3,5), (4,5),( 6,5)} = 11

Step 2: Verify that the given two events are complementary events are not.

            NOTE:  The given two events are compliment to each other

              So,  Probability of getting getting 5 = \frac{n(F)}{n(T)}

                                                                      = \frac{11}{36}

                  Let us consider an event B of not getting number 5 either time

                  The probability of not getting 5 either time P(B) = 1 - P(A)

                                                                                      P(B) = 1 - \frac{11}{36}

                                                                                              = \frac{11 - 36}{36}

                                                                                       P(B) = \frac{25}{36}