1. **State the problem:** Simplify the expression $$[(-7 + \frac{12}{5}) \cdot \left(-\frac{15}{4}\right) \cdot \left(-\frac{5}{2}\right)] : \left(\frac{5}{4}\right)$$ 2. **Rewrite the expression clearly:** $$\left(-7 + \frac{12}{5}\right) \times \left(-\frac{15}{4}\right) \times \left(-\frac{5}{2}\right) \div \frac{5}{4}$$ 3. **Calculate inside the parentheses:** $$-7 + \frac{12}{5} = \frac{-35}{5} + \frac{12}{5} = \frac{-35 + 12}{5} = \frac{-23}{5}$$ 4. **Substitute back:** $$\frac{-23}{5} \times \left(-\frac{15}{4}\right) \times \left(-\frac{5}{2}\right) \div \frac{5}{4}$$ 5. **Multiply the first two fractions:** $$\frac{-23}{5} \times \left(-\frac{15}{4}\right) = \frac{-23 \times -15}{5 \times 4} = \frac{345}{20}$$ 6. **Multiply the result by the third fraction:** $$\frac{345}{20} \times \left(-\frac{5}{2}\right) = \frac{345 \times -5}{20 \times 2} = \frac{-1725}{40}$$ 7. **Divide by the last fraction:** $$\frac{-1725}{40} \div \frac{5}{4} = \frac{-1725}{40} \times \frac{4}{5} = \frac{-1725 \times 4}{40 \times 5}$$ 8. **Simplify numerator and denominator:** $$\frac{-1725 \times 4}{40 \times 5} = \frac{-6900}{200}$$ 9. **Simplify the fraction by dividing numerator and denominator by 20:** $$\frac{\cancel{-6900}^{\div 20}}{\cancel{200}^{\div 20}} = \frac{-345}{10}$$ 10. **Final answer:** $$\boxed{-\frac{345}{10}}$$ or $$-34.5$$ This is the simplified value of the given expression.