C

- Hướng dẫn giải

Chọn  C

$\underset{x\to +\infty }{\lim }x\left(\sqrt{x^2+5}-x\right)=\underset{x\to +\infty }{\lim }x\frac{x^2+5-x^2}{\sqrt{x^2+5}+x}=\underset{x\to +\infty }{\lim }\frac{5x}{x\sqrt{1+\frac{5}{x^2}}+x}=\frac{5}{1+1}=\frac{5}{2}$