Let's take a look at your question.
We have to say if x<0 or not.
First statement
Since the power is an odd number, then it implies that x will also have the same sign, so x<0. Therefore, this statement is sufficient.1) x^5 < 0.
Second statement
This equation will lead us to $$x^5+x+1=0$$ $$x^5+x=-1$$ $$x\left(x^4+1\right)=-1 $$ $$x\left(x^4+1\right)=negative\ number .$$ Now, x^4+1 is always positive, so it implies that x must be negative, that is to say, x<0.2) x^5 + x + 1 = 0.
Therefore, this statement is sufficient.
In conclusion, each statement alone is sufficient. The answer is the option D.
I hope it helps you. <i class="em em-smiley"></i>
