Answer
Neither even nor odd
Work Step by Step
If $f(-x)=f(x)$ then the function is even.
If $f(-x)=-f(x)$ then the function is odd.
If $f(-x)\neq f(x)$ and $f(-x)\neq -f(x)$ then the function is neither even nor odd.
$$f(x)=x^4-5x+8$$ $$f(-x)=(-x)^4-5(-x)+8=x^4+5x+8=-(-x^4-5x-8)$$ It is neither $f(x)$ not $f(-x)$, so, neither even nor odd.
