5. 若 $\alpha \in\left(0, \frac{\pi}{2}\right)$, 且 $\sin ^{2} \alpha+\cos 2 \alpha=\frac{1}{4}$, 则 $\tan \alpha$ 的值等于
由 $\sin ^{2} \alpha+\cos 2 \alpha=\frac{1}{4}$ 得 $\sin ^{2} \alpha+\cos ^{2} \alpha-\sin ^{2} \alpha=\cos ^{2} \alpha=\frac{1}{4} \because \alpha \in\left(0, \frac{\pi}{2}\right), \therefore \cos \alpha=\frac{1}{2}$,

$\therefore \alpha=\frac{\pi}{3}, \therefore \tan \alpha=\tan \frac{\pi}{3}=\sqrt{3}$.