5. In the coordinate plane, a point whose both coordinates are integers is called an integer point. We use $I$ to denote the set of all lines, $M$ to denote the set of lines passing through exactly one integer point, $N$ to denote the set of lines not passing through any integer point, and $P$ to denote the set of lines passing through infinitely many integer points. Then the number of correct statements among the following expressions:
(1) $M \cup N \cup P=I$;
(2) $N \neq \Phi$;
(3) $M \neq \Phi$;
(4) $P \neq \Phi$.

is
(A) 1 ;
(B) 2 ;
(C) 3 ;
(D) 4 .
5. (D)

The line $y=\frac{1}{2}$ does not pass through any integer points, so expression (2) is correct;
The line $y=\sqrt{2} x$ passes through infinitely many points, exactly one of which is the integer point $(0, 0)$, so expression (3) is correct;
The line $y=x$ passes through multiple integer points, so expression (4) is correct; we will prove that if
$$
a x+b y+c=0
$$

passes through two integer points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$,
then it passes through infinitely many integer points
$$
\left(x_{2}+k\left(x_{2}-x_{1}\right), y_{1}+k\left(y_{2}-y_{1}\right)\right), k \in \mathbb{Z}.
$$

In fact,
$$
\begin{aligned}
& a\left[\left(x_{1}+k\left(x_{2}-x_{1}\right)\right]+b\left[y_{1}+k\left(y_{2}-y_{1}\right)\right]+c\right. \\
= & a x_{1}+b y_{1}+c+k\left(a x_{2}+b y_{2}+c\right)-k\left(a x_{1}+b y_{1}+c\right) \\
= & 0,
\end{aligned}
$$

hence the answer is (D).