$f$ is not even or odd.
Work Step by Step
$f(x) = 1+3x^3 -x^5$ lets calculate $f(-x)$ $f(-x)=1+3(-x)^3 -(-x)^5=1+3(-1)^3x^3 -(-1)^5x^5$ $=1-3x^3 +x^5\ne f(x) \ne -f(x)$ Therefore $f$ is not even or odd.
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