Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 660: 22

$-7$

Simplifying each term and then combining like terms, the given expression, $ \sqrt[3]{27}-5\sqrt[3]{8} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{(3)^3}-5\sqrt[3]{(2)^3} \\\\= 3-5\cdot2 \\\\= 3-10 \\\\= -7 .\end{array}