Solution:

$Point =\left(x_{1}, y_{1}\right)=(4,5)$

$Slope of the line 7 x-5 y=420 is,$

$m=-\frac{a}{b}=-\frac{7}{-5}=\frac{7}{5}$

$\therefore Slope of the required line is,$

$m_{1}=-\frac{1}{m}=\frac{-5}{7}$

$\therefore equation is,$

$\quad y-y_{1}=m_{1}\left(x-x_{1}\right)$ $\therefore y-5=\frac{-5}{7}(x-4)$

$\therefore 5 x+7 y-55=0$