5.4. What is the maximum volume of the pyramid $S A B C$, where $A B=3, A C=5$ and $\sin \angle B A C = \frac{3}{5}$, and all lateral edges $S A, S B, S C$ form the same angle with the base plane, not exceeding $60^{\circ} ?$
Answer. $\frac{5 \sqrt{174}}{4} \approx 16.49$.