1. **State the problem:** Simplify the expression $$\frac{a^8 - 4a^5 - 5a^3}{a^2}$$. 2. **Recall the rule for dividing powers with the same base:** $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply the rule to each term in the numerator divided by $$a^2$$:** $$\frac{a^8}{a^2} - \frac{4a^5}{a^2} - \frac{5a^3}{a^2} = a^{8-2} - 4a^{5-2} - 5a^{3-2}$$ 4. **Simplify the exponents:** $$a^6 - 4a^3 - 5a^1$$ 5. **Write the final simplified expression:** $$a^6 - 4a^3 - 5a$$ This is the simplified form of the given expression.