Explanation

(c)
Given equation of lines are
$5x + 3y - 7 = 0$ …(i)
and $15x + 9y + 14 = 0$ or $5x + 3y + \frac{14}{3} = 0$ …(ii)
∵ Lines (i) and (ii) are parallel and $c_{1}\$ and $c_{2}$ are of opposite signs, therefore these lines are on opposite sides of the origin
So, the distance between them is
$\left| \frac{c_{1}}{\sqrt{a_{1}^{2} + b_{1}^{2}}} \right| + \left| \frac{c_{2}}{\sqrt{a_{2}^{2} + b_{2}^{2}}} \right| = \left| - \frac{7}{\sqrt{5^{2} + 3^{2}}} \right| + \left| \frac{14}{3\sqrt{5^{2} + 3^{2}}} \right| = \left| - \frac{7}{\sqrt{34}} \right| + \left| \frac{14}{3\sqrt{34}} \right| = \frac{35}{3\sqrt{34}}$