#### Answer

$(-\infty, -5) \cup (-1, +\infty)$

#### Work Step by Step

$(x+1)(x+5)\gt0$
$(x+1)(x+5) =0$
$x=-1$ or $x=-5$
Plot these numbers on a number line,split them into intervals, take one test point from each interval, and check them to see if they are true. If they are true, then it is a solution.
In this case, it is
$(-\infty, -5) \cup (-1, +\infty)$