5. The altitudes of triangle $A B C$ intersect at a point $H$. Find $\angle A C B$ if it is known that $A B=C H$. Explain your reasoning.
We observe that $\angle A C F=\angle A B E$.
Since $A B=C H$, we have $\angle C H E=\angle E A B$, [1 mk] and, in particular, $A E=E H$. [1 mk]
Since $\angle A E H=90^{\circ}$ this means $\angle E A H=45^{\circ}$
Also $\angle A G C=90^{\circ}$ inside $\triangle A C G$
thus $\angle A C B=45^{\circ}$. [1 mk]