It is not clear to me why x^5+5 needs an absolute value when there is no value for x that would be x^10+10x^5+25 negative.
Try x = -2. x^5 + 5 is negative but as you said, x^{10} + 10 x^5 + 25 is not.
It is not clear to me why x^5+5 needs an absolute value when there is no value for x that would be x^10+10x^5+25 negative.
Try x = -2. x^5 + 5 is negative but as you said, x^{10} + 10 x^5 + 25 is not.