\(\sqrt {1-x} \le \sqrt[4]{{x + 5}}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{{{\left( {1-x} \right)}^2} \le x + 5,}\\{1-x \ge 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left\{ \begin{array}{l}{x^2}-3x-4 \le 0,\\x \le 1\end{array} \right.\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\left\{ \begin{array}{l}x \in \left[ {-1;4} \right],\\x \in \,\left( {-\infty ;1} \right]\end{array} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x \in \left[ {-1;\,1} \right].\)
Ответ: \(\left[ {-1;1} \right].\)