Simplified from of [ ( 5 x^ - 3/5 )^ - 5/3 ]^ - 5 = ?

Answer: Option D

$$\begin{array}{rl}& {\left[{\left(\text{root}5\text{of}{x}^{-\frac{3}{5}}\right)}^{-\frac{5}{3}}\right]}^{-5}\\ & ={\left[{\left(x^{-\frac{3}{25}}\right)}^{-\frac{5}{3}}\right]}^{-5}\\ & ={\left[\left(x^{\frac{1}{5}}\right)\right]}^{-5}\\ & =x^{-\frac{1}{5}\times 5}\\ & =x^{-1}\\ & =\frac{1}{x}\end{array}$$