\[\frac{1}{256}, - \frac{1}{128},\ \frac{1}{64},\ \ldots.\]
\[q = - \frac{1}{128}\ :\frac{1}{256} = \frac{- 256}{128} = - 2;\]
\[b_{5} = b_{1} \cdot q^{4} = \frac{1}{256} \cdot 16 = \frac{1}{16}.\]
\[Ответ:\ \ q = - 2;\ \ \ \ b_{5} = \frac{1}{16}.\]