Geometric progression

The formula for the sum of the first n terms of geometric progression is
$S_n = \dfrac{a_1(1 - r^n)}{1 - r}$
 

All we need to do is to find the first term a₁ and the common ratio r.
 

To find the common ratio use the formula
$a_n = a_m r^{n - m}$

$a_6 = a_3 r^{6 - 3}$
 

With r known, you can solve for a₁ using the formula:
$a_n = a_1 r^{n - 1}$

$a_6 = a_1 r^{6 - 1}$
 

With your a₁ and r known, you can now calculate the sum S₅.