Question: Use the properties of limits to find the given limit. lim x\to\infty \frac{5x^5 + 9x^4 - 7x^3}{25 - 5x^5} lim x\to\infty \frac{5x^5 + 9x^4 - 7x^3}{25 - 5x^5} = \square (Type an integer or a simplified fraction.)

1. **State the problem:** Find the limit $$\lim_{x \to \infty} \frac{5x^5 + 9x^4 - 7x^3}{25 - 5x^5}$$. 2. **Identify the highest power of $x$ in numerator and denominator:** The highest power is $x^5$. 3. **Divide numerator and denominator by $x^5$ to simplify:** $$\lim_{x \to \infty} \frac{\frac{5x^5}{x^5} + \frac{9x^4}{x^5} - \frac{7x^3}{x^5}}{\frac{25}{x^5} - \frac{5x^5}{x^5}} = \lim_{x \to \infty} \frac{5 + \frac{9}{x} - \frac{7}{x^2}}{\frac{25}{x^5} - 5}$$ 4. **Evaluate the limit as $x \to \infty$:** Terms with $\frac{1}{x^n}$ go to zero. $$= \frac{5 + 0 - 0}{0 - 5} = \frac{5}{-5}$$ 5. **Simplify the fraction:** $$= \frac{\cancel{5}}{\cancel{-5}} = -1$$ **Final answer:** $$\boxed{-1}$$