Write the equation of the line that is perpendicular to the given line and that passes through the given point

-x+5y=14 (-5,-2)

Slope-intercepted form:
y=mx+b
In this equation; "m" is the slope of the line.

We have this equation:
-x+5y=14
It´s slope-intercepted form would be:
-x+5y=14
5y=x+14
y=1/5 x+14/5  (slope-intercepted form)

And the slope in this line is: m=1/5

A line perpendicular to this line will be the next slope:
m`=-1/m; 
m´=-1/(1/5)=-5

Point-slope form:we need a point (x₀,y₀) and the slope:
y-y₀=m(x-x₀)
We have a point (-5,-2) and the slope, m=-5
y+2=-5(x+5)
y+2=-5x-25
y=-5x-25-2
y=-5x-27  (slope-intercepted form)

the equation would be y=-5x-27