Find a line perpendicular to – 5 x – 4 y = 19 that passes through ( – 5 , 11 )

Solve  – 5 x – 4 y = 19   for y to obtain the slope:  -5x - 19 = 4y, and so
the slope is (-5/4).

A line perpendicular to – 5 x – 4 y = 19  must have a slope which is the negative reciprocal of this (-5/4).  That would be (+4/5).

Using the point-slope form of the eqn of a str line:

y-11 = (4/5)(x-[-5]), or   (4/5)(x+5).  This could, of course, be written in other (but equivalent) forms.