$(5+\sqrt[3]{2})$
Let assume that $(5+\sqrt[3]{2})$ is irrational
Subtract 5 from given number, considering 5 is rational number .as we know , Difference of two rational numbers is a rational.
$(5+\sqrt[3]{2})-5$ is rational
$\Rightarrow \sqrt[3]{2}$ is rational.
(product of two rational numbers is rational)
but, $\sqrt[3]{2}$ is irrational
which is contradictory to our assumption.
So $(5+\sqrt[3]{2})$ is irrational.