Answer
$x=-4$
Work Step by Step
Using the properties of equality, the given equation, $
\sqrt[3]{x-4}-5=-7
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{x-4}=-7+5
\\\\
\sqrt[3]{x-4}=-2
.\end{array}
Raising both sides of the equation above to the third power, then the solution/s is/are
\begin{array}{l}\require{cancel}
x-4=-8
\\\\
x=-8+4
\\\\
x=-4
.\end{array}