Answer
The lines are perpendicular to each other.
Work Step by Step
RECALL:
(1) Parallel lines have the same slope.
(2) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other.)
(3) The slope-intercept form of a line's equation is $y=mx + b$ where $m$=slope and $(0, b)$ is the line's y-intercept.
Write both equations in slope-intercept form to obtain:
First Equation:
$y+5=-x
\\y+5-5=-x-5
\\y=-x-5$
The slope of this line is $-1$.
Second Equation:
$x-y=2
\\x-y-x=2-x
\\-y=2-x
\\-y=-x+2
\\-1(-y)=-1(-x+2)
\\y=x-2$
The slope of this line is $1$.
Since $-1(1)=-1$, the two lines are perpendicular to each other.