\[b_{1} = 27;\ \ q = - \frac{1}{3}:\]
\[S_{5} = \frac{27 \cdot \left( \left( - \frac{1}{3} \right)^{5} - 1 \right)}{- \frac{1}{3} - 1} =\]
\[= \frac{27 \cdot \left( - \frac{1}{243} - 1 \right)}{- \frac{4}{3}} =\]
\[= \frac{27 \cdot 3 \cdot \left( - \frac{244}{243} \right)}{- 4} =\]
\[= \frac{81 \cdot 244}{4 \cdot 243} = \frac{61}{3} = 20\frac{1}{3}.\]