\[\boxed{\mathbf{14}\mathbf{.}}\]
\[1)\ b_{4} = 88\ \ и\ \ q = 2\]
\[b_{4} = b_{1} \bullet q^{3} \Longrightarrow b_{1} = \frac{b_{4}}{q^{3}} = \frac{88}{2^{3}} =\]
\[= \frac{88}{8} = 11\]
\[S_{5} = \frac{b_{1}\left( 1 - q^{n} \right)}{1 - q} = \frac{11\left( 1 - 2^{5} \right)}{1 - 2} =\]
\[= - 11(1 - 32) = 11 \bullet 31 = 341\]
\[Ответ:\ \ 341.\]
\[2)\ b_{1} = 11\ \ и\ \ b_{4} = 88;\]
\[b_{4} = b_{1} \bullet q^{3} \Longrightarrow q = \sqrt[3]{\frac{b_{4}}{b_{1}}} =\]
\[= \sqrt[3]{\frac{88}{11}} = \sqrt[3]{8} = 2\]
\[S_{5} = \frac{b_{1}\left( 1 - q^{n} \right)}{1 - q} = \frac{11\left( 1 - 2^{5} \right)}{1 - 2} =\]
\[= - 11(1 - 32) = 11 \bullet 31 = 341\]
\[Ответ:\ \ 341.\]