score ranking no tie, if tie order by score submit date
Order by Score in descending order, and by SubmitDate in ascending order, then use a variable to give correlative numbers to each row:

mysql&gt; SET @Rank := 0;
Query OK, 0 rows affected (0.00 sec)

mysql&gt; SELECT *, @Rank := @Rank + 1 AS Rank FROM ranking ORDER BY Score DESC, SubmitDate ASC;
+----+-------+-------+---------------------+------+
| Id | Name  | Score | SubmitDate          | Rank |
+----+-------+-------+---------------------+------+
|  4 | Bash  |   102 | 2014-08-04 21:37:17 |    1 |
|  1 | Ida   |   100 | 2014-08-01 21:37:17 |    2 |
|  2 | Boo   |    99 | 2014-08-02 21:37:17 |    3 |
|  3 | Lala  |    99 | 2014-08-03 21:37:17 |    4 |
|  5 | Assem |    99 | 2014-08-05 21:37:17 |    5 |
+----+-------+-------+---------------------+------+
5 rows in set (0.00 sec)