Answer
$r=\dfrac{30}{1-5\sin \theta}$
Work Step by Step
The equation of conic with eccentricity $e$ and directrix $x=k$ leads to focus can be written as:
$r=\dfrac{ke}{1+e \cos \theta}$
Given: $e=5,k=6$
Then $y=-6$
Thus, the equation (1) can be written as:
$r=\dfrac{ke}{1+e \cos \theta}=\dfrac{30}{1-5\sin \theta}$