5. Given that $\alpha, \beta$ are the roots of the equation $x^{2}+x-1=0$. Then the value of $\alpha^{16}-987 \beta+411$ is ( ).
(A) 2006
(B) 2007
(C) 2008
(D) 2009
5.C.

From the given, we have $\alpha^{2}=1-\alpha$ and $\alpha+\beta=-1$. Therefore,
$$
\begin{array}{l}
\alpha^{4}=(1-\alpha)^{2}=1-2 \alpha+\alpha^{2}=2-3 \alpha, \\
\alpha^{8}=(2-3 \alpha)^{2}=4-12 \alpha+9 \alpha^{2}=13-21 \alpha, \\
\alpha^{16}=(13-21 \alpha)^{2}=169-546 \alpha+441 \alpha^{2}=610-987 \alpha .
\end{array}
$$

Thus, $\alpha^{16}-987 \beta+411=(610-987 \alpha)-987 \beta+411$
$$
=1021-987(\alpha+\beta)=1021+987=2008 .
$$