Chọn phương án A.

\(\begin{aligned}
\lim\limits_{x\to-\infty}\dfrac{\sqrt{x^2+1}-x}{5-2|x|}&=\lim\limits_{x\to-\infty}\dfrac{-x\sqrt{1+\dfrac{1}{x^2}}-x}{5+2x}\\
&=\lim\limits_{x\to-\infty}\dfrac{-x\left(\sqrt{1+\dfrac{1}{x^2}}+1\right)}{x\left(\dfrac{5}{x}+2\right)}\\
&=\lim\limits_{x\to-\infty}\dfrac{-\left(\sqrt{1+\dfrac{1}{x^2}}+1\right)}{\dfrac{5}{x}+2}\\
&=\dfrac{-\left(\sqrt{1+0}+1\right)}{0+2}=-1.
\end{aligned}\)