1. **State the problem:** Simplify the expression $$\left(\frac{5}{6}\right)^2 \times (-36) + \frac{5}{7} \div \left(-\frac{25}{14}\right)$$. 2. **Recall the rules:** - To square a fraction, square numerator and denominator separately: $$\left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2}$$. - Multiplying a fraction by an integer: multiply numerator by the integer. - Dividing by a fraction is the same as multiplying by its reciprocal. 3. **Calculate the square:** $$\left(\frac{5}{6}\right)^2 = \frac{5^2}{6^2} = \frac{25}{36}$$ 4. **Multiply by -36:** $$\frac{25}{36} \times (-36) = \frac{25 \times \cancel{36}}{\cancel{36}} \times (-1) = 25 \times (-1) = -25$$ 5. **Divide the fractions:** $$\frac{5}{7} \div \left(-\frac{25}{14}\right) = \frac{5}{7} \times \left(-\frac{14}{25}\right) = \frac{5 \times (-14)}{7 \times 25} = \frac{-70}{175}$$ 6. **Simplify the fraction:** $$\frac{-70}{175} = \frac{\cancel{-70}^{-14}}{\cancel{175}^{35}} = \frac{-14}{35}$$ 7. **Add the results:** $$-25 + \left(-\frac{14}{35}\right) = -25 - \frac{14}{35} = -\frac{25 \times 35}{35} - \frac{14}{35} = -\frac{875}{35} - \frac{14}{35} = -\frac{889}{35}$$ **Final answer:** $$-\frac{889}{35}$$