5. In $\triangle A B C$, medians $A D$ and $C F$ intersect at point $G$. If $\angle A F G=45^{\circ}, \angle A G C=60^{\circ}$, then the degree measure of $\angle A C F$ is ( ).
(A) $30^{\circ}$
(B) $45^{\circ}$
(C) $60^{\circ}$
(D) $75^{\circ}$
5.D.

As shown in Figure 5, draw $C M \perp A G$ at point $M$, and connect $M F$. Let $G M = 1$, then $C G = 2, F G = 1$. Therefore,
$$
F G = G M .
$$

Thus, 
$$
\begin{array}{l}
\angle M F C \\
= \angle G C M \\
= 30^{\circ},
\end{array}
$$
$\angle M F A = \angle M A F = 15^{\circ}$.
Hence, $A M = F M = C M$.
Therefore, $\angle A C M = 45^{\circ}$.
So, $\angle A C F = 75^{\circ}$.