5. In a sequence of numbers $x_{1}, x_{2}, \cdots$, it is known that $x_{1}=1$, and for $k \geqslant 2$,
$$
x_{k}=x_{k-1}+1-4\left(\left[\frac{k-1}{4}\right]-\left[\frac{k-2}{4}\right]\right) \text {. }
$$

Then $x_{2010}=(\quad$.
(A) 1
(B) 2
(C) 3
( D) 4
(2010, National Junior High School Mathematics Competition)
Hint From the given, we have
$$
\begin{array}{l}
x_{1}=1, x_{2}=2, x_{3}=3, x_{4}=4, x_{5}=1, \\
x_{6}=2, x_{7}=3, x_{8}=4, \cdots \cdots
\end{array}
$$

Since $2010=4 \times 502+2$, therefore,
$$
x_{2010}=x_{2}=2 \text{. }
$$

So the answer is (B).