(12 points)\\
Let the sides opposite to angles $A, B, C$ of $\triangle ABC$ be $a, b, c$ respectively. Given
$$\sin C \sin(A - B) = \sin B \sin(C - A)$$
(1) Prove: $2a^2 = b^2 + c^2$;\\
(2) If $a = 5, \cos A = \frac{25}{31}$, find the perimeter of $\triangle ABC$.