5. If $a=2000 x+2015, b=2000 x+2016, c=2000 x+2017$, then the value of the algebraic expression $\sqrt{a^{2}+b^{2}+c^{2}-a b-b c-c a}$ is ( )
(A) 1
(B) $\sqrt{2}$
(C) $\sqrt{3}$
(D) $\sqrt{6}$
Answer: (C)
Solution:
$$
\begin{aligned}
& a^{2}+b^{2}+c^{2}-a b-b c-c a \\
= & \frac{1}{2}\left[(a-b)^{2}+(b-c)^{2}+(c-a)^{2}\right] \\
= & \frac{1}{2}\left[(-1)^{2}+(-1)^{2}+2^{2}\right] \\
= & 3 .
\end{aligned}
$$

So the original expression $=\sqrt{3}$.
Therefore, the correct choice is (C).