[tex]\displaystyle\bf\\\left \{ {{b_{5}=18 } \atop {b_{3} =162}} \right. \\\\\\:\left \{ {{b_{1} \cdot q^{4} =18} \atop {b_{1} \cdot q^{2} =162}} \right. \\--------\\q^{2} =\frac{1}{9} \\\\q_{1} =\frac{1}{3} \ \ \ ; \ \ \ \boxed{q_{2} =-\frac{1}{3} < 0}\\\\\\b_{1} =162:q^{2} =162:\frac{1}{9} =162\cdot 9=1458[/tex]

[tex]\displaystyle\bf\\S_{5} =\frac{b_{1} \cdot(1-q^{5} )}{1-q} =\frac{1458\cdot\bigg[1-\bigg(-\dfrac{1}{243} \bigg)\bigg]}{1-\bigg(-\dfrac{1}{3} \bigg)} =\frac{1458\cdot\bigg(1+\dfrac{1}{243} \bigg)}{1+\dfrac{1}{3} } =\\\\\\=\frac{1458\cdot\dfrac{244}{243} }{\dfrac{4}{3} }=\frac{6\cdot244\cdot 3}{4}=18\cdot 61=1098[/tex]