\\\\(5^m \\div 5^{-3} = 5^5\\\\)\\\\(\\Rightarrow \\displaystyle 5^m \\div \\frac{1}{5^3} = 5^5\\\\)\\\\( \\Rightarrow 5^m \ imes 5^3 = 5^5\\\\)\\\\(\\Rightarrow 5^{m + 3} = 5^5\\\\)\\\\(\\Rightarrow m + 3 = 5\\\\)\\\\(\\Rightarrow m = 5 - 3 = 2\\\\)