\(B=\left(-5\right)^0+\left(-5\right)^1+\left(-5\right)^2+...+\left(-5\right)^{2017}\)
\(-5B=\left(-5\right)^1+\left(-5\right)^2+...+\left(-5\right)^{2018}\)
\(-5B-B=\left(-5\right)^1+\left(-5\right)^2+...+\left(-5\right)^{2018}-\)\(\left[\left(-5\right)^0+\left(-5\right)^1+\left(-5\right)^2+...+\left(-5\right)^{2017}\right]\)
\(-6B=\left(-5\right)^0-\left(-5\right)^{2018}\)
\(B=\left(5^{2018}-1\right):6\)