Verified answer

[tex]\displaystyle\bf\\b_{1} =\frac{1}{216} \\\\q=-6\\\\\\b_{5} =b_{1} \cdot q^{4} =\frac{1}{216} \cdot(-6)^{4} =\frac{1}{216} \cdot 1296=6\\\\\\\boxed{b_{5} =6}\\\\\\S_{5} =\frac{b_{1}\cdot(q^{5} -1) }{q-1} =\frac{\dfrac{1}{216}\cdot\Big[(-6)^{5}-1\Big] }{-6-1} =\frac{\dfrac{1}{216}\cdot(-7776-1) }{-7} =\\\\\\=\frac{\dfrac{1}{216}\cdot(-7777) }{-7} =\frac{1}{216}\cdot 1111=5\frac{31}{1080}[/tex]