I. x > 0
If x is greater than 1 (which is greater than 0), $x^5$ will be greater than $x^3$. Thus, (I) could be true.
E.g., if x = 2, $x^5$ = 32 and $x^3$ = 8 ---> 32 > 8

II. x < 0
If x is less than 0 but greater than -1, $x^5$ will be greater than $x^3$. Thus, (II) could be true.
E.g., if x = -0.5, $x^5$ = -0.03125 and $x^3$ = -0.125 ---> -0.03125 > -0.125

III. x < -1
If x is less than -1, $x^5$ will always be less than $x^3$. Thus, (III) cannot be true.
E.g., if x = -2, $x^5$ = -32 and $x^3$ = -8 ---> -32 < -8