How do you solve abs(-5x-3)=8?

$x = - \frac{11}{5}$ or $x = - 1$
$| - 5 x - 3 | = 8$ meaans
either $- 5 x - 3 = 8$ i.e. $- 5 x = 11$ i.e. $x = - \frac{11}{5}$
or $- 5 x - 3 = - 8$ i.e. $- 5 x = - 8 + 3 = - 5$ i.e. $x = - 1$