Answer
$f^{-1}(x)=x+5$
(the inverse is blue on the graph)
Work Step by Step
Step 1: Replace $f(x)$ with $y$.
$y=x-5$
Step 2: Interchange $x$ and $y$.
$x=y-5$
Step 3: Solve the equation for $y$.
$ x=y-5,\qquad$ ... add 5,
$x+5=y$
Step 4: Replace y with the notation $f^{-1}(x)$.
$f^{-1}(x)=x+5$
Graphing $f(x)=x-5,$
the y-intercept is at $(0,-5)$,
the x-intercept is when $\left[\begin{array}{l}
0=x-5\\
x=5
\end{array}\right]$, at the point ($5,0$)
Plot the two points and draw a straight line through them.
Graphing $f^{-1}(x)=x+5,$
the y-intercept is at $(0,5)$,
the x-intercept is when $\left[\begin{array}{l}
0=x+5\\
x=-5
\end{array}\right]$, at the point ($-5,0$)
Plot the two points and draw a straight line through them.
You may want to graph the line $y=x$ with a dashed line, to show the symmetry.