#### Answer

$\left( -\infty, -\dfrac{13}{5} \right) \cup \left( 3, \infty\right)$

#### Work Step by Step

Since for any $a\gt0$, $|x|\gt a$ implies $x\gt a$ or $x\lt-a,$ then the given inequality, $
|5x-1|\gt14
,$ is equivalent to
\begin{array}{l}\require{cancel}
5x-1\gt14 \text{ OR } 5x-1\lt-14
.\end{array}
Solving each inequality results to
\begin{array}{l}\require{cancel}
5x-1\gt14
\\\\
5x\gt14+1
\\\\
5x\gt15
\\\\
x\gt\dfrac{15}{5}
\\\\
x\gt3
\\\\\text{ OR }\\\\
5x-1\lt-14
\\\\
5x\lt-14+1
\\\\
5x\lt-13
\\\\
x\lt-\dfrac{13}{5}
.\end{array}
Hence, the solution is the interval $
\left( -\infty, -\dfrac{13}{5} \right) \cup \left( 3, \infty\right)
.$