Answer
$r=\dfrac{10}{5-\cos \theta}$
Work Step by Step
The equation of conic with eccentricity $e$ and directrix $x=k$ leads to focus can be written as:
$r=\dfrac{ke}{1+e \cos \theta}$ ....(1)
Given: $e=\dfrac{1}{5}$
Thus, the equation (1) can be written as:
$r=\dfrac{ke}{1+e \cos \theta}=\dfrac{2}{1-(\dfrac{1}{5})\sin \theta}$
or, $r=\dfrac{10}{5-\cos \theta}$