Answer
$5x-8y=-40$
Work Step by Step
Solving for y, we find the slope of $ 8\mathrm{x}+5\mathrm{y}=3:$
$8x+5y=3$
$5y=-8x+3$
$y=\displaystyle \frac{-8}{5}x+\frac{3}{5}$
$m_{1}=-\displaystyle \frac{8}{5}$
The line perpendicular to it has slope $m= -\displaystyle \frac{1}{m_{1}}=\frac{5}{8}.$
Use $y-y_{1}=m(x-x_{1}) \ \ \ $ (the point-slope form) and rearrange :
$y-5=\displaystyle \frac{5}{8}(x-0)\qquad/\times 8$
$8(y-5)=5x$
$8y-40=5x$
$-40=5x-8y$
$5x-8y=-40$
