STRATEGY: As with all GRE Multiple Choice questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can easily test x-values to see whether they satisfy the given inequality, and then eliminate answer choices accordingly.
Now we should give ourselves 15-20 seconds to identify a faster approach.
There's also an algebraic approach, but I feel that it might take a little longer. So, I'll start testing x-values.

NOTE: We can speed up our calculations by recognizing we can factor the left side of the inequality to get x⁵(x² - 1) < 0

When I scan the answer choices, I see that testing x = -2 will enable me to eliminate some answer choices (regardless of whether it satisfies the inequality)
Plug x = -2 into our inequality to get: (-2)⁵(2² - 1) < 0
I know that (-2)⁵ is negative, and since (-2)² is greater than 1, I know that (-2)² - 1 is positive.
So our inequality becomes (some negative number)(some positive number)< 0
Since this is TRUE, we know that x = -2 is a solution to the given inequality.
This means we can eliminate answer choices B, D and E since they don't include x = -2 as a solution.

Now let's test x = 0.5
We get: (0.5)⁵((0.5)² - 1) < 0
I know that (0.5)⁵ must be positive, and since (0.5)² is less than 1, I know that (0.5)² - 1 is negative.
So our inequality becomes (some positive number)(some negative number) < 0
Since this is TRUE, we know that x = 0.5 is a solution to the given inequality.
This means we can eliminate answer choice A since it doesn't include x = 0.5 as a solution.

By the process of elimination, the correct answer is C