What is the equation of the line that goes through (-1,-1) and is perpendicular to y=5x+3

Perpendicular lines have slopes that multiply to -1

y=mx+b
slope=m
y=5x+3

5=slope
5 times what=-1
divide both sides by 5
what=-1/5

the equation of a line that passes through the point (x1,y1) and has a slope of m is
y-y1=m(x-x1)
given

m=-1/5
point=(-1,-1)

y-(-1)=-1/5(x-(-1))
y+1=-1/5(x+1)
y+1=-1/5x-1/5
y=-1/5x-6/5
1/5x+y=-6/5
x+5y=-6

the euation is
y+1=-1/5(x+1) or
y=-1/5x-6/5 or
x+5y=-6 (all same equation but different forms)

This is Point Intercept Form for the equation that is perpendicular to y=5x+3
y+1=1/5(x+1)