A body of mass m rises to a height h = $\frac{\mathrm{R}}{5}$ from the Earth's surface where R is Earth's radius. If g is acceleration due to gravity at the Earth's surface, the increase in potential energy 

$$\begin{gathered} u_i=-\frac{GMm}{R} \\ {u}_f=-\frac{GMm}{R+h} \left(h=\frac{R}{5}\right) \end{gathered}$$

Increase in gravitational potential energy

              = $\left[\frac{\mathrm{GMm}}{\mathrm{R}+{\displaystyle \frac{\mathrm{R}}{5}}}\right] - [-\frac{\mathrm{GMm}}{\mathrm{R}}]$

               = $\frac{\mathrm{GMm}}{\mathrm{R}}-\frac{\mathrm{GMm}\times 5}{6\mathrm{R}}$

                = $\frac{\mathrm{GMm}}{\mathrm{R}}[1-\frac{5}{6}] = \frac{\mathrm{GMm}}{\mathrm{R}}\times \frac{1}{6}$

                 = $\frac{{\mathrm{mgR}}^2}{6\mathrm{R}} = \frac{1}{6}\mathrm{mgR} = \frac{5}{6}\mathrm{mgh}. [\mathrm{R} = 5\mathrm{h}]$