#### Answer

$a_{n}=3n+2$

#### Work Step by Step

The sequence starts with
$a_{1}=5=3+2$
So then
$a_{2}=5+3=3+3+2=3*2+2$
$a_{3}=8+3=3+3+3+2=3*3+2$
$a_{4}=11+3=3+3+3+3+2=3*4+2$
etc...
Note that the first part number being multiplied to $3$ is the same as the term number.
Thus, if $n$ is the term number, then the explicit formula is
$a_{n}=3n+2$