This function is undefined when x = 0. Since x = 0 is in the domain of f, this is a possible inflection point. To determine if x = 0 is a real inflection point, we need to inspect the sign of f " to either side.
When x is greater than zero,
is also greater than zero, so
When x is less than zero,
is also less than zero because of the odd numbers in the fractional exponent (the cube root of a negative number is negative, and raising a negative number to the 5th power is negative). Therefore
Since f " changes sign at x = 0, this is an inflection point. Here's the graph: