#### Answer

$58\sqrt{3}$

#### Work Step by Step

Simplifying each term and then combining like terms, the given expression, $
5\sqrt{12}+16\sqrt{27}
,$ is equivalent to
\begin{array}{l}\require{cancel}
5\sqrt{4\cdot3}+16\sqrt{9\cdot3}
\\\\=
5\sqrt{(2)^2\cdot3}+16\sqrt{(3)^2\cdot3}
\\\\=
5\cdot2\sqrt{3}+16\cdot3\sqrt{3}
\\\\=
10\sqrt{3}+48\sqrt{3}
\\\\=
58\sqrt{3}
.\end{array}