Answer
perpendicular
Work Step by Step
Using $y=mx+b$ where $m$ is the slope, the slope of the first equation,
\begin{array}{l}\require{cancel}
x+y=5
\\\\
y=-x+5
\end{array}
is $m_1=
-1
.$
Using $y=mx+b$ where $m$ is the slope, the slope of the second equation,
\begin{array}{l}\require{cancel}
x-y=1
\\\\
-y=-x+1
\\\\
y=x-1
\end{array}
is $m_2=
1
.$
Since $m_1\cdot m_2=-1,$ then the given lines are $\text{
perpendicular
.}$