$x\geq6$ or $x\leq4$.
Work Step by Step
$|x-5|\geq1$ implies $x-5\geq1\\x\geq6$ or $x-5\leq-1\\x\leq4$. Thus $x\geq6$ or $x\leq4$. Then, by using a graphing utility, the solution set is attached.
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