The distance of the points of intersection of the lines 
$2x - 3y + 5 = 0$ and $3x + 4y = 0$ from the line  $5x - 2y = 0$ is-

$\begin{array}{c} 2 x-3 y+5=0 \\ 3 x+4 y=0 \end{array}$

the point of intersection $\left(-\frac{20}{17}, \frac{15}{17}\right)$

$\begin{aligned} \therefore \text { distance } & \frac{\left|5 \times\left(-\frac{20}{17}\right)-2\left(\frac{15}{17}\right)\right|}{\sqrt{5^{2}+(-2)^{2}}} \\ = & \frac{130}{17 \sqrt{29}} \end{aligned}$