Answer
$f(x)=-2x^5+3x^3-2x+1$
Work Step by Step
The function $f$ has an odd degree, therefore it has different behavior when $x\rightarrow -\infty$ and $x\rightarrow \infty$.
The sign of the leading coefficient decides if $f(x)\rightarrow -\infty$ or $f(x)\rightarrow \infty$ when $x\rightarrow-\infty$ and $x\rightarrow \infty$.
Because $f(x)\rightarrow \infty$ when $x\rightarrow -\infty$, it means that the leading coefficient is negative.
An example of such a function is:
$$f(x)=-2x^5+3x^3-2x+1.$$
The graph of the function confirms our conclusion.
