Answer
The function is odd and has symmetry with respect to the origin.
Work Step by Step
f(x)=x$^3$-5x
f(-x)=(-x)$^3$-5(-x)
f(-x)=-x$^3$+5x
-f(x)=-(x$^3$-5x)
-f(x)=-x$^3$+5x
Since f(-x)=-f(x), the function is odd. Odd functions have symmetry with respect to the origin.