Two adjacent sides of a parallelogram \( PQRS \) are given by \( \overrightarrow{PQ}=\hat{j}+\hat{k} \) and \( \overrightarrow{PS}=\hat{i}-\hat{j} \). If the side \( PS \) is rotated about the point \( P \) by an acute angle \( \alpha \) in the plane of the parallelogram so that it becomes perpendicular to the side \( PQ \), then \( \sin^{2}\!\left(\dfrac{5\alpha}{2}\right)-\sin^{2}\!\left(\dfrac{\alpha}{2}\right) \) is equal to:
