A set of five dice is marked 1 to 6, but instead of commonly used spots bears Arabic digits .
After a single roll of dice they are arranged to represent a 5-digit number.
It is found that this number fullfils ALL of the following conditions:
1. There is no descending order of digits within this number.
2. No digit is repeated more than twice within this number.
3. At least one of the digits in the number is bigger than 5.

How many such 5 - digit numbers exist?