Answer
Since $x^4\geq0$, then $x^4+1\geq 1$, and so $x^4+1\lt -5$ is never true and therefore has no solution.
Work Step by Step
We know that for any real number $x$, $x^4\geq0$.
This means that
$x^4+1\geq1$ for any real number $x$.
Thus,
$x^4+1\lt -5$ is never true and therefore has no solution.
