Answer
The solution is $x=-14$.
Work Step by Step
The given equation is
$\Rightarrow -5=\sqrt[3]{10x+15}$
Cube each side of the equation.
$\Rightarrow (-5)^3=(\sqrt[3]{10x+15})^3$
Simplify.
$\Rightarrow -125=10x+15$
Subtract $15$ from each side.
$\Rightarrow -125-15=10x+15-15$
Simplify.
$\Rightarrow -140=10x$
Divide each side by $10$.
$\Rightarrow -14=x$
Check $x=-14$.
$\Rightarrow -5=\sqrt[3]{10x+15}$
$\Rightarrow -5=\sqrt[3]{10(-14)+15}$
$\Rightarrow -5=\sqrt[3]{-140+15}$
$\Rightarrow -5=\sqrt[3]{-125}$
$\Rightarrow -5=\sqrt[3]{(-5)^3}$
$\Rightarrow -5=-5$
True.
Hence, the solution is $x=-14$.
