Solve the Inequality: Understanding |5x-10| > 15

To solve the inequality $\left|5x-10\right| > 15$, we rewrite it as two separate inequalities:

• First inequality: $5x - 10 > 15$
• Second inequality: $5x - 10 < -15$

Let's solve each one:

For the first inequality $5x - 10 > 15$:
Add 10 to both sides: $5x > 25$
Divide both sides by 5: $x > 5$

For the second inequality $5x - 10 < -15$:
Add 10 to both sides: $5x < -5$
Divide both sides by 5: $x < -1$

Combining these solutions, we have:
$x > 5$ or $x < -1$

Therefore, the correct statement regarding the solution set is: $x > 5$ or $x < -1$.