Answer
$0.5$
Work Step by Step
$x$ is "approaching $-\infty$" means that $x$ is assuming negative values of greater and greater magnitude.
See table below.
As we make $x$ assumes negative values of greater and greater magnitude, the function value approaches the value $0.5$.
So, we write
$\displaystyle \lim_{x\rightarrow-\infty}\frac{x^{5}-1000x^{4}}{2x^{5}+1000}=0.5$
