Answer
$$y=\frac{5+5^x\cdot \:2^{2+x}}{10^x-1}$$
Work Step by Step
Switching the elements of the domain and the range (in other words, the dependent and independent variables), we find that the inverse is:
$$x=\log _{10}\left(\frac{y+5}{y-4}\right) \\ y=\frac{5+5^x\cdot \:2^{2+x}}{10^x-1}$$