#### Answer

$x=-1$

#### Work Step by Step

Using exponents, the given equation, $
2^{x+5}=16
,$ is equivalent to
\begin{array}{l}\require{cancel}
2^{x+5}=2^4
.\end{array}
Since the bases are the same, the exponents can be equated. Hence,
\begin{array}{l}\require{cancel}
x+5=4
\\\\
x=4-5
\\\\
x=-1
.\end{array}