1. The problem is to solve the equation $$| |x| | = 5$$. 2. The absolute value function $|x|$ returns the non-negative value of $x$. Applying absolute value twice, as in $| |x| |$, is equivalent to a single absolute value because $|x|$ is already non-negative. 3. Therefore, $$| |x| | = |x|$$. 4. The equation simplifies to $$|x| = 5$$. 5. The rule for absolute value equations is: if $$|x| = a$$ where $a \geq 0$, then $$x = a$$ or $$x = -a$$. 6. Applying this rule, we get $$x = 5$$ or $$x = -5$$. 7. We do not keep the absolute value sign after applying the rule because the equation is solved for $x$. Final answer: $$x = 5 \text{ or } x = -5$$.