5. On the arc $A C$ of the circumcircle of an equilateral triangle $A B C$, a point $M$ is chosen such that the lengths of the segments $M A$ and $M C$ are 2 and 3, respectively. The line $B M$ intersects the side $A C$ at point $N$. Find the length of the segment $M N$ and the side of the triangle $A B C$.
Answer: $A B=\sqrt{19} ; M N=\frac{6}{5}$.