#### Answer

$p=9$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given radical equation, $
\sqrt[3]{p+5}=\sqrt[3]{2p-4}
,$ raise both sides of the equation to the third power. Then use properties of equality to isolate and solve the variable. Finally, do checking of the solution/s with the original equation.
$\bf{\text{Solution Details:}}$
Raising both sides of the equation to the third power results to
\begin{array}{l}\require{cancel}
\left(\sqrt[3]{p+5}\right)^3=\left(\sqrt[3]{2p-4}\right)^3
\\\\
p+5=2p-4
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
p-2p=-4-5
\\\\
-p=-9
\\\\
p=9
.\end{array}
Upon checking, $
p=9
$ satisfies the original equation.