詳解：無窮極限問題處理方法說明如下，分子分母各自除 \({x^2}\)

\( \lim\limits_{x \to \infty } \frac{{4{x^2} - x + 5}}{{2{x^2} + 8x + 5}} = \lim\limits_{x \to \infty } \frac{{4 - \frac{x}{{{x^2}}} + \frac{5}{{{x^2}}}}}{{2 + \frac{{8x}}{{{x^2}}} + \frac{5}{{{x^2}}}}} = \lim\limits_{x \to \infty } \frac{{4 - \frac{1}{x} + \frac{5}{{{x^2}}}}}{{2 + \frac{8}{x} + \frac{5}{{{x^2}}}}}\)

當 \(x \to \infty \) 時，後面分式部分均會趨近0，僅留下各自領導係數 \(\lim\limits_{x \to \infty } \frac{{4 - \frac{1}{x} + \frac{5}{{{x^2}}}}}{{2 + \frac{8}{x} + \frac{5}{{{x^2}}}}} = \lim\limits_{x \to \infty } \frac{{4 - 0 + 0}}{{2 + 0 + 0}} = \frac{4}{2} = 2\)

故選(C)