[tex]5^{-101} - 5^{-103} = \\ = 5^{-101} - 5^{(-101-2)} = \\ = 5^{-101} - 5^{[(-101)+(-2)]} = \\ = 5^{-101} - 5^{-101}\cdot 5^{-2}} = \\ = 5^{-101}(1-5^{-2})= \\ = \frac{1}{5^{101}}(1- \frac{1}{5^2})= \frac{1}{5^{101}}(\frac{5^2-1}{5^2})= \frac{25-1}{5^{101}\cdot5^2}= \frac{24}{5^{101+2}}=\boxed{\frac{24}{5^{103}}}[/tex]
