5. As shown in Figure $3, A B$ is the diameter of the semicircle $\odot O$, $A C$ and $A D$ are both chords, and $\angle B A C = \angle C A D$. Which of the following equations is true? ( ).
(A) $A C^{2} = A B \cdot A D$
(B) $A B \cdot A D > A C^{2}$
(C) $A B + A D = 2 A C$
(D) $A B + A D < 2 A C$
5. D.

As shown in Figure 6, draw $O M \perp A D$ at point $M$, intersecting $A C$ at point $N$, and connect $O C$.
It is easy to see that $O C \parallel A D$
$$
\begin{array}{r}
\Rightarrow \angle C O N=\angle C O M \\
=\angle O M A=90^{\circ} .
\end{array}
$$

It is also easy to see that
$$
N C > O C = \frac{1}{2} A B, A N > A M = \frac{1}{2} A D \text {. }
$$

Therefore, $A B + A D < 2 A C$, and $A B \cdot A D < A C^{2}$.