select      col1,col2,col3
           ,min(date) as minDate
           ,max(date) as maxDate

from       (select      *
                       ,row_number () over 
                        (
                            partition by    col1,col2
                            order by        date
                        ) as rn_part_1_2

                       ,row_number () over 
                        (
                            partition by    col1,col2,col3
                            order by        date
                        ) as rn_part_1_2_3                            

            from        mytable
            ) t

group by    col1,col2,col3
           ,rn_part_1_2 - rn_part_1_2_3

order by    col1,col2
           ,minDate
;

+------+------+------+------------+------------+
| col1 | col2 | col3 |  mindate   |  maxdate   |
+------+------+------+------------+------------+
| A    | X    |    5 | 2016-02-01 | 2016-02-04 |
| A    | X    |    6 | 2016-03-01 | 2016-03-01 |
| A    | X    |    5 | 2016-04-01 | 2016-04-01 |
| A    | Y    |    5 | 2016-04-02 | 2016-04-03 |
+------+------+------+------------+------------+