Answer :
When a line is given in the form
[tex]y=mx+q[/tex]
The slope of the line is m. So, in this case, the slope of [tex]y=x-5[/tex] is 1.
Given a slope [tex]m[/tex], you find the slope of a perpendicular line [tex]m'[/tex] by imposing
[tex]m\cdot m' = -1[/tex]
So, if the given line has slope 1, a perpendicular line has slope [tex]m'[/tex] given by
[tex]1 \cdot m' = -1[/tex]
and thus [tex]m'=-1[/tex]
So, we want a line with slope -1 and passing through (12,-1). Using the fomula
[tex]y-y_0=m(x-x_0)[/tex]
we get
[tex]y-(-1)=-1(x-12) \iff y+1=-x+12 \iff y=-x+11[/tex]