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The formula for $S(n)$ is given by,

$S(n) = a \dfrac{r^n - 1}{r - 1}$

where $a$ is the first term and $r$ is the common ratio. Therefore,

$\dfrac{S(20)}{S(10)} = \dfrac{r^{20} - 1}{r^{10} - 1} = 10$

Using the difference between squares identity, and simplifying, we obtain,

$\dfrac{ (r^{10}-1)(r^{10}+1) }{r^{10} - 1} = r^{10} + 1 = 10$

So that, $r^{10} = 9$ .

Hence, $r^5 = \sqrt{9} = 3$

Now,

$\begin{aligned} \dfrac{S(40)}{S(5) } &= \dfrac{ r^{40} - 1 }{r^{5} - 1} = \dfrac{ (r^{10})^4 - 1}{r^5 - 1} \\ &= \dfrac{ 9^4 - 1}{3 - 1} = \dfrac{ 6560 }{2} = 3280 \\ \end{aligned}$