5. Let $A, B$ be the two foci of a hyperbola, and $C$ be a point on the hyperbola. It is known that the three sides of $\triangle A B C$ form an arithmetic sequence, and $\angle A C B=120^{\circ}$. Then the eccentricity of the hyperbola is $\qquad$.
5. $\frac{7}{2}$.

According to the problem, we can set $|A C|+|A B|=2|B C|$, and $|A C|^{2}+|B C|^{2}-|A B|^{2}=2|A C| \cdot|B C|$. $\cos 120^{\circ}$, from this we know $|A C|:|A B|:|B C|=3: 7: 5$. Thus, the eccentricity of the hyperbola is $\frac{7}{5-3}=\frac{7}{2}$.