#### Answer

$-7$

#### Work Step by Step

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}