1. **State the problem:** Evaluate the expression $$\frac{5}{6} - \frac{3}{5} \times \left(-\frac{4}{5}\right)$$. 2. **Recall the order of operations:** Multiplication comes before subtraction. 3. **Multiply the fractions:** $$\frac{3}{5} \times \left(-\frac{4}{5}\right) = \frac{3 \times (-4)}{5 \times 5} = \frac{-12}{25}$$ 4. **Rewrite the expression:** $$\frac{5}{6} - \left(-\frac{12}{25}\right) = \frac{5}{6} + \frac{12}{25}$$ 5. **Find a common denominator:** The denominators are 6 and 25. The least common denominator (LCD) is $$6 \times 25 = 150$$. 6. **Convert each fraction to have denominator 150:** $$\frac{5}{6} = \frac{5 \times 25}{6 \times 25} = \frac{125}{150}$$ $$\frac{12}{25} = \frac{12 \times 6}{25 \times 6} = \frac{72}{150}$$ 7. **Add the fractions:** $$\frac{125}{150} + \frac{72}{150} = \frac{125 + 72}{150} = \frac{197}{150}$$ 8. **Simplify if possible:** 197 and 150 have no common factors other than 1, so the fraction is in simplest form. **Final answer:** $$\frac{197}{150}$$ or as a mixed number $$1 \frac{47}{150}$$.