Answer
$y=-\frac{2}{5}x-\frac{11}{5}$
Work Step by Step
Step 1. Find the slope of the existing line $5x-2y=6$ as $m_1=\frac{5}{2}$
Step 2. The slope of the line perpendicular to the above line will be $m=-\frac{1}{m_1}=-\frac{2}{5}$
Step 3. Together with the known point $(2,-3)$, we can write the new line equation as $y+3=-\frac{2}{5}(x-2)$ or $y=-\frac{2}{5}x-\frac{11}{5}$
