#### Answer

$a_{1}=3;$
$a_{2}=4;$
$a_{3}=7;$
$a_{4}=12;$
$a_{5}=19$

#### Work Step by Step

$a_{1}=\dfrac {1^{3}+8}{1+2}=3;$
$a_{2}=\dfrac {2^{3}+8}{2+2}=4;$
$a_{3}=\dfrac {3^{3}+8}{3+2}=7;$
$a_{4}=\dfrac {4^{3}+8}{4+2}=12;$
$a_{5}=\dfrac {5^{3}+8}{5+2}=19$