\(M=5^{2016}-5^{2015}-5^{2014}-...-5-1\)
=>\(5M=5\left(5^{2016}-5^{2015}-5^{2014}-...-5-1\right)\)
=>\(5M=5^{2017}-5^{2016}-5^{2015}-...-5^2-5\)
=>\(5M-M=\left(5^{2017}-5^{2016}-5^{2015}-...-5^2-5\right)-\left(5^{2016}-5^{2015}-5^{2014}-...-5-1\right)\)
=>\(4M=5^{2017}-2.5^{2016}+1\)
=>\(M=\frac{5^{2017}-2.5^{2016}+1}{4}\)