Answer
neither.
Work Step by Step
Step 1. Replace $x$ with $-x$, we have $f(-x)=(-x)^4-5(-x)+8=(x)^4+5(x)+8\ne f(x)$, thus it is not even.
Step 2. Replace $x$ with $-x$, we have $f(-x)=(-x)^4-5(-x)+8=(x)^4+5(x)+8\ne-f(x)$, thus it is not odd.