1. **State the problem:** Simplify the expression $$\frac{25x^7}{-5x^2}$$. 2. **Recall the laws of exponents and division:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Simplify the coefficients:** $$\frac{25}{-5} = -5$$. 4. **Simplify the variable part using the exponent rule:** $$\frac{x^7}{x^2} = x^{7-2} = x^5$$. 5. **Combine the simplified parts:** $$-5 \times x^5 = -5x^5$$. 6. **Final answer:** $$\boxed{-5x^5}$$.