Answer
$f$ cannot be written in the form $f(x)=a(x-h)^5+k$.
Work Step by Step
The graph of $f(x)=x^5-3x^2+2x+1$ is as shown.
Notice that there is a part of the graph that is increasing and then decreasing which is makes the graph not strictly increasing, then $f$ cannot be written in the form $f(x)=a(x-h)^5+k$.
