F(x) = x^5  - c \\ 
 F^' (x) = 5x^4  \\ 
 x_{n + 1}  = {x_n  - \frac{{F(x)}}{{F^' (x)}} }= {x_n  - {\frac{{x_n^5  - c}}{{5x_n^4 }}} }= {\frac{{5x_n^5  - x_n^5  + c}}{{5x_n^4 }}} = \frac{{4x_n^5  + c}}{{5x_n^4 }} = \frac{1}{5}\left( {4x_n  + \frac{c}{{x_n^4 }}} \right) \\ 

\]