#### Answer

$n=21$

#### Work Step by Step

Multiplying both sides by the $LCD=
3
$ and then using the properties of equality, the value of the variable that satisfies the given equation, $
\dfrac{2n-5}{3}=\dfrac{n+1}{3}+5
,$ is
\begin{array}{l}\require{cancel}
1(2n-5)=1(n+1)+3(5)
\\\\
2n-5=n+1+15
\\\\
2n-n=1+15+5
\\\\
n=21
.\end{array}