1. **State the problem:** Simplify the expression $$\frac{3}{5} - \frac{5}{4} \left[ \frac{2}{3} - \frac{7}{5} \left(- \frac{2}{3} \right) \right]$$. 2. **Recall the order of operations:** First, solve inside the brackets, then multiply, and finally subtract. 3. **Simplify inside the inner bracket:** $$\frac{7}{5} \left(- \frac{2}{3} \right) = - \frac{14}{15}$$ 4. **Evaluate the expression inside the square brackets:** $$\frac{2}{3} - \left(- \frac{14}{15} \right) = \frac{2}{3} + \frac{14}{15}$$ 5. **Find common denominator for addition:** $$\frac{2}{3} = \frac{10}{15}$$ 6. **Add the fractions:** $$\frac{10}{15} + \frac{14}{15} = \frac{24}{15}$$ 7. **Simplify the fraction:** $$\frac{24}{15} = \frac{8}{5}$$ 8. **Multiply by $$\frac{5}{4}$$:** $$\frac{5}{4} \times \frac{8}{5} = \frac{\cancel{5}}{4} \times \frac{8}{\cancel{5}} = \frac{8}{4} = 2$$ 9. **Subtract from $$\frac{3}{5}$$:** $$\frac{3}{5} - 2 = \frac{3}{5} - \frac{10}{5} = \frac{3 - 10}{5} = -\frac{7}{5}$$ **Final answer:** $$-\frac{7}{5}$$