Answer
Domain: $(-\infty,\ 4)$
Work Step by Step
We need to find the domain of the given function:
$f(x)=\log_{5}(8-2x)$
We know that we can't take the log of a negative number, so:
$8-2x\gt 0$
$8\gt 2x$
$4\gt x$
Thus the domain is: $(-\infty,\ 4)$