Answer
{$ \pm \sqrt 5i,\pm 1$}
Work Step by Step
Since, $u^2+4u=5$ or, $u^2+4u-5=0$
Factorize the expression as follows: $(u+5)(u-1)=0$
or, $u=${$-5,1$}
Replace $u$ with $x^2$, we have
$x^2=-5 \implies x=\pm \sqrt {-5}$
or, $x=\pm \sqrt 5i$
and $x^2=1$
This implies that $x= \pm \sqrt 5i,\pm 1$
Hence, our solution set is $x=${$ \pm \sqrt 5i,\pm 1$}