5. || $\log _{2} x|+1| \geqslant \log _{2} 4 x$ The solution is

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5. $\left\{x \left\lvert\, 0<x \leqslant \frac{\sqrt{2}}{2}\right.\right\}$

The set of all $x$ such that $0 < x \leqslant \frac{\sqrt{2}}{2}$.