1. **State the problem:** Simplify the expression $$-\frac{2}{9} + 2 \frac{1}{2} \div \left(-\frac{2}{5}\right)$$. 2. **Convert mixed number to improper fraction:** $$2 \frac{1}{2} = \frac{5}{2}$$. 3. **Rewrite the expression:** $$-\frac{2}{9} + \frac{5}{2} \div \left(-\frac{2}{5}\right)$$. 4. **Division of fractions rule:** $$a \div b = a \times \frac{1}{b}$$. 5. **Apply division:** $$\frac{5}{2} \div \left(-\frac{2}{5}\right) = \frac{5}{2} \times \left(-\frac{5}{2}\right) = -\frac{25}{4}$$. 6. **Rewrite the expression:** $$-\frac{2}{9} + \left(-\frac{25}{4}\right) = -\frac{2}{9} - \frac{25}{4}$$. 7. **Find common denominator:** $$\text{LCM}(9,4) = 36$$. 8. **Convert fractions:** $$-\frac{2}{9} = -\frac{8}{36}, \quad -\frac{25}{4} = -\frac{225}{36}$$. 9. **Add fractions:** $$-\frac{8}{36} - \frac{225}{36} = -\frac{233}{36}$$. 10. **Final answer:** $$\boxed{-\frac{233}{36}}$$. This is the simplified form of the original expression.