Answer
odd.
Work Step by Step
Step 1. Replace $x$ with $-x$, we have $f(-x)=(-x)^5-2(-x)^3=-(x)^5+2(x)^3\ne f(x)$, thus it is not even.
Step 2. Replace $x$ with $-x$, we have $f(-x)=(-x)^5-2(-x)^3=-(x)^5+2(x)^3=-f(x)$, thus it is odd.
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