Answer
The linear function is $f(x)=-x+2$.
Work Step by Step
Rewrite as shown below.
$f(0)=2$ as $(0,2)$
and $f(5)=-3$ as $(5,-3)$
Let $(x_1,y_1)=(0,2)$ and $(x_2,y_2)=(5,-3)$.
Slope
$\Rightarrow m =\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m =\frac{-3-2}{5-0}$
Simplify.
$\Rightarrow m =\frac{-5}{5}$
$\Rightarrow m =-1$
The point-slope form.
$\Rightarrow y-y_1=m(x-x_1)$
Substitute all the values.
$\Rightarrow y-(2)=-1(x-0)$
Simplify.
$\Rightarrow y-2=-x$
Add $2$ to each side.
$\Rightarrow y-2+2=-x+2$
Simplify.
$\Rightarrow y=-x+2$
Hence, the linear function is $f(x)=-x+2$.