Answer
$-1$
Work Step by Step
Recall:
(1) $\lim _{x\rightarrow c}\left( f\left( x\right) \right) ^{n}=\left( \lim _{x\rightarrow c}f\left( x\right) \right) ^{n}$
(2) $\lim _{x\rightarrow c}f(x) = f(c)$
Use the rules above to have:
$ \lim _{x\rightarrow -1}\left( 2x+1\right) ^{\frac {5}{3}}
\\=\left( \lim _{x\rightarrow -1}\left( 2x+1\right) \right) ^{\frac {5}{3}}
\\=\left(2(-1)+1\right)^{5/3}
\\=\left( -2+1\right) ^{\frac {5}{3}}
\\=-1^{\frac {5}{3}}
\\=-1$
