To find $ a_{ 5 } $ we use formula

$$ \color{blue}{a_n = a_1 \cdot r^{n-1}}$$

In this example we have $ a_1 = 5 ~~,~~ r = 3 ~~\text{and}~~ n = 5 $. After substituting these values to above formula, we obtain:

$$ \begin{aligned} a_n &= a_1 \cdot r^{n-1} \\ a_{ 5 } &= 5 \cdot 3^{ 5 - 1} \\ a_{ 5 } &= 5 \cdot 81 \\ a_{ 5 } &= 405 \end{aligned}$$

The first few terms of this sequence are:

$$ 5, ~~~15, ~~~45, ~~~135 . . . $$

Geometric sequences