Divisibility!

$\large\left\lfloor \frac{5!}{7} \right\rfloor \times \left\lceil \frac{5!}{7} \right\rceil$ $\frac{5!}{7}=\frac{120}{7}=17+\frac{1}{7}$ $\Rightarrow \large\left\lfloor \frac{5!}{7} \right\rfloor \times \left\lceil \frac{5!}{7} \right\rceil=(17)\times(18)=2*9*17$ The value of the given expression is expressed as $2*9*17$ which is divisible by 9. Therefore, the answer is $\boxed{9}$ . :D

Floor & Ceiling Functions At A Glance : The floor and ceiling functions map a real number to the largest previous or the smallest following integer, respectively. More precisely, $floor(x) = \lfloor x\rfloor$ is the largest integer not greater than x and $ceiling(x) = \lceil x \rceil$ is the smallest integer not less than x.

The Floor Function is also known as the Greatest Integer Funtion.

Source: Wikipedia - Floor&Ceiling Functions