\(a_1=20;\ r=\dfrac{1}{4};\ n=5\\\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\S_5=\dfrac{20\cdot\left[1-\left(\dfrac{1}{4}\right)^5\right]}{1-\dfrac{1}{4}}=\dfrac{20\cdot\left(1-\dfrac{1}{1024}\right)}{\dfrac{3}{4}}\)
\(=\dfrac{20\cdot\dfrac{1023}{1024}}{\dfrac{3}{4}}=\dfrac{20460}{1024}\cdot\dfrac{4}{3}=\dfrac{6820}{256}=\dfrac{1705}{64}=26\dfrac{41}{64}\\\\Answer:\boxed{S_5=26\frac{41}{64}}\)
