Given below are two statements:
Statement I : $\lim _{x \rightarrow 0}\left(\frac{\tan ^{-1} x+\log _e \sqrt{\frac{1+x}{1-x}}-2 x}{x^5}\right)=\frac{2}{5}$
Statement II: $\lim _{x \rightarrow 1}\left(x^{\frac{2}{1-x}}\right)=\frac{1}{e^2}$
In the light of the above statements, choose the correct answer from the options given below