Let D be the domain of the function $\mathrm{f}\left(\mathrm{x}\right)={\sin }^{-1}\left({\log }_{3\mathrm{x}}\left(\frac{6+2{\log }_3\mathrm{x}}{-5\mathrm{x}}\right)\right)$. If the range of the function $\mathrm{g}:\mathrm{D}\to \mathrm{R}$ defined by $\mathrm{g}\left(\mathrm{x}\right)=\mathrm{x}-\left[\mathrm{x}\right],\left(\right[\mathrm{x}]$ is the greatest integer function), is $(\mathrm{\alpha },\mathrm{\beta }),$ then ${\mathrm{\alpha }}^2+\frac{5}{\mathrm{\beta }}$ is equal to