#### Answer

$\dfrac {87}{60}$

#### Work Step by Step

$\sum ^{5}_{i=1}\left( i+1\right) ^{-1}=\dfrac {1}{1+1}+\dfrac {1}{2+1}+\dfrac {1}{3+1}+\dfrac {1}{4+1}+\dfrac {1}{5+1}=\dfrac {1}{2}+\dfrac {1}{3}+\dfrac {1}{4}+\dfrac {1}{5}+\dfrac {1}{6}=\dfrac {87}{60}$