a^{-2} - 10a^{-1}b^{-1} + 25b^{-2} / a^{-1} - 5b^{-1}

The expression can be simplified by recognizing the numerator as a perfect square trinomial: $$(a^{-1} - 5b^{-1})^2$$.

Thus, the expression becomes $$\frac{(a^{-1} - 5b^{-1})^2}{a^{-1} - 5b^{-1}}$$.

Simplifying, we get $$a^{-1} - 5b^{-1}$$.