#### Answer

The solution is $(-\infty,-3)\cup(1,\infty)$

#### Work Step by Step

$5|x+1|\gt10$
Take $5$ to divide the right side:
$|x+1|\gt\dfrac{10}{5}$
$|x+1|\gt2$
Solving this absolute value inequality is equivalent to solving two separate inequalities, which are:
$x+1\gt2$ and $x+1\lt-2$
$\textbf{Solve the first inequality:}$
$x+1\gt2$
Take $1$ to the right side:
$x\gt2-1$
$x\gt1$
$\textbf{Solve the second inequality:}$
$x+1\lt-2$
Take $1$ to the right side:
$x\lt-2-1$
$x\lt-3$
Expressing the solution in interval notation:
$(-\infty,-3)\cup(1,\infty)$