To solve the equation \(\frac{\sqrt[3]{x+4}}{x^{3}+5} = 0\), we need to find the value of \(x\) that makes the numerator zero, since a fraction is zero when its numerator is zero and the denominator is not zero. Therefore, we solve \(\sqrt[3]{x+4} = 0\) and ensure that \(x^3 + 5 \neq 0\).
Step 1: Simplify the Expression
The given expression is:
\[
\frac{\sqrt[3]{x+4}}{x^{3}+5}
\]
There are no obvious simplifications or factorizations for the numerator \(\sqrt[3]{x+4}\) or the denominator \(x^3 + 5\) that can be performed without additional information or constraints on \(x\). Therefore, the expression is already in its simplest form.
Final Answer
The expression \(\frac{\sqrt[3]{x+4}}{x^{3}+5}\) is already in its simplest form. Thus, the final answer is: