$\Large{\frac{625^{\cos^2{x}}}{25^{\cos{x}}}}$ $=$ $25^{(2\cos^2{x} - \cos{x})}$ $=$ $1$ $\implies$ $2 \cos^2{x} - \cos{x}$ $=$ $0$ , temos: $\cos{x} = 0$ $\implies$ $x = \{\frac{\pi}{2}, \frac{3\pi}{2} \}$ . Para $\cos{x}$ $\neq$ $0$, temos: $2 \cos{x} = 1$ $\implies$ $\cos{x} = \frac{1}{2}$ $\implies$ $x = \{\frac{\pi}{3}, \frac{5\pi}{3} \}$ No intervalo $0 \leq x \leq \frac{\pi}{2}$ temos $x = \{\frac{\pi}{3}, \frac{\pi}{2} \}$ $\implies$ $\boxed{\large{\frac{\pi}{3} + \frac{\pi}{2} = \frac{5\pi}{6}}}$