If y=y(x), y ∈[0, (π)/2) is the solution of the differential equation sec y (d y)/(d x)- sin (x+y)- sin (x-y)=0, with y(0)=0, then 5 y^′((π)/2) is…

If $\displaystyle y=y(x), \quad y \in\left[0, \frac{\pi}{2}\right)$ is the solution of the differential equation $\displaystyle \sec y \frac{d y}{d x}-\sin (x+y)-\sin (x-y)=0$, with $\displaystyle y(0)=0$, then $\displaystyle 5 y^{\prime}\left(\frac{\pi}{2}\right)$ is equal to \_\_\_\_.