1. **State the problem:** Simplify the expression $$\frac{10x^8}{2x^5}$$. 2. **Recall the division rule for exponents:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply the rule to the coefficients:** $$\frac{10}{2} = 5$$. 4. **Apply the rule to the variable part:** $$x^{8-5} = x^3$$. 5. **Combine the results:** $$5x^3$$. **Final answer:** $$5x^3$$.