math

We are given that $30^\circ$ is equal to $5$ students.

We need to find the total number of students who took part in the survey. All we need to do is find the ratio of the $30^\circ$ portion to the whole circle, then multiply it by $5$.

$30 : 5 = 360 : x$
$30x = 1800$

$x = 60$.

Therefore, there are $\boxed{60}$ students participating in the survey.