\(=\lim\limits\dfrac{n^2+an+5-n^2-1}{\sqrt{n^2+an+5}+\sqrt{n^2+1}}=\lim\limits\dfrac{an+4}{\sqrt{n^2+an+5}+\sqrt{n^2+1}}\)
\(=\lim\limits\dfrac{\dfrac{an}{n}+\dfrac{4}{n}}{\sqrt{\dfrac{n^2}{n^2}+\dfrac{an}{n^2}+\dfrac{5}{n^2}}+\sqrt{\dfrac{n^2}{n^2}+\dfrac{1}{n^2}}}=\dfrac{a}{1+1}=\dfrac{a}{2}\)
\(\lim\limits\left(u_n\right)=-1\Rightarrow\dfrac{a}{2}=-1\Rightarrow a=-2\)