5. Given a two-digit number $\overline{p q}$, such that the quadratic function $y=x^{2}+q x+p$ intersects the $x$-axis at two distinct points $A$ and $B$, with the vertex at $C$, and $S_{\triangle A B C} \leqslant 1$. Then the number of such two-digit numbers is
(A) 1
(B) 2
(C) 3
(D) 4
5. D.

Let $A\left(x_{1}, 0\right)$ and $B\left(x_{2}, 0\right)\left(x_{1} \neq x_{2}\right)$. Then $x_{1}$ and $x_{2}$ are the two distinct real roots of the equation $x^{2}+q x+p=0$.
Thus, $x_{1}+x_{2}=-q, x_{1} x_{2}=p$.
Therefore, $S_{\triangle A B C}=\frac{1}{2}\left|x_{1}-x_{2}\right|\left|y_{c}\right|$
$$
=\frac{1}{2} \sqrt{q^{2}-4 p}\left|\frac{4 p-q^{2}}{4}\right| \leqslant 1 \text {. }
$$

Hence, $q^{2}-4 p=1,2,3,4$.
Since $q^{2}-4 p \equiv 0$ or $1(\bmod 4)$, we have,
$$
(p, q)=(2,3),(3,4),(6,5),(8,6) .
$$