#### Answer

$x=-6$ and $x=1$

#### Work Step by Step

$x+5=\dfrac{6}{x}$
Multiply the whole equation by $x$:
$x\Big(x+5=\dfrac{6}{x}\Big)$
$x^{2}+5x=6$
Take the $6$ to the left side of the equation:
$x^{2}+5x-6=0$
Solve this equation by factoring:
$(x+6)(x-1)=0$
Set each factor equal to $0$ and solve each individual equation:
$x+6=0$
$x=-6$
$x-1=0$
$x=1$
The original equation is not undefined for neither of the values of $x$ found, so the solutions are:
$x=-6$ and $x=1$