\[b_{1} = - 750;b_{2} = - 150;\]
\[q = \frac{b_{2}}{b_{1}} = - \frac{150}{750} = - \frac{1}{5};\]
\[S_{5} = \frac{b_{1}\left( q^{n} - 1 \right)}{q - 1} =\]
\[= \frac{- 750\left( \left( - \frac{1}{5} \right)^{5} - 1 \right)}{- \frac{1}{5} - 1} =\]
\[= \frac{- 750 \cdot \left( - \frac{1}{3125} - 1 \right)}{- \frac{6}{5}} =\]
\[= \frac{- 750 \cdot \left( - \frac{3126}{3125} \right)}{- \frac{6}{5}} =\]
\[= 625 \cdot \left( - \frac{3126}{3125} \right) =\]
\[= - \frac{3126}{5} = - 625,2.\]
\[Ответ:\ - 625,2.\]