a: \(2014^0+\left(-5\right)+2010=1-5+2010=2006\)
b: \(=\left(4+\dfrac{7}{13}+\dfrac{6}{13}\right)^3=5^3=125\)
c: \(\left(-\dfrac{2}{3}\right)^{2015}\cdot x=\left(-\dfrac{2}{3}\right)^{2017}\)
\(\Leftrightarrow x=\left(-\dfrac{2}{3}\right)^{2017}:\left(-\dfrac{2}{3}\right)^{2015}=\left(-\dfrac{2}{3}\right)^2=\dfrac{4}{9}\)