5.3. What is the maximum volume of the pyramid $S A B C$, where $A B=3, A C=5$ and $\sin \angle B A C = \frac{4}{5}$, and all lateral edges $S A, S B, S C$ form the same angle with the base plane, not exceeding $60^{\circ}$?
Answer. $\frac{5 \sqrt{39}}{2} \approx 15.61$.