Hey there!
First, we want to put the equation of this first line in slope-intercept form.
5y=x-5
We divide both sides by 5.
y=1/5x-1.
The slope of a perpendicular is line is the negative reciprocal of the slope of the original line. The slope of a line perpendicular to a line with the equation y=1/2x would be -2, because you flip the numerator and denominator and then make it negative.
So, this means that the slope of the line perpendicular to the line y=1/5x-1 is -5. So, here's our equation so far.
y= -5x+b
Now, we need to find the b. To do this, we can plug in this point (-1,0) that this perpendicular line goes through and solve for b.
0=-5(-1)+b
0=5+b
b= -5
So, this gives us the equation y= -5x-5
Have a wonderful day!