1. **State the problem:** Find the value of $$\left( \frac{5}{12} - \frac{7}{9} \cdot 0.25 \right)^{-1} \cdot 1 \frac{2}{9}$$. 2. **Rewrite the mixed number:** Convert $$1 \frac{2}{9}$$ to an improper fraction: $$1 \frac{2}{9} = \frac{9}{9} + \frac{2}{9} = \frac{11}{9}$$. 3. **Calculate the product inside the parentheses:** Multiply $$\frac{7}{9}$$ by $$0.25$$ (which is $$\frac{1}{4}$$): $$\frac{7}{9} \cdot \frac{1}{4} = \frac{7}{36}$$. 4. **Subtract the fractions inside the parentheses:** $$\frac{5}{12} - \frac{7}{36}$$. Find a common denominator, which is 36: $$\frac{5}{12} = \frac{15}{36}$$. So, $$\frac{15}{36} - \frac{7}{36} = \frac{8}{36} = \frac{2}{9}$$. 5. **Apply the exponent -1:** $$\left( \frac{2}{9} \right)^{-1} = \frac{9}{2}$$. 6. **Multiply by the improper fraction:** $$\frac{9}{2} \cdot \frac{11}{9} = \frac{11}{2} = 5.5$$. 7. **Check the answer:** The problem states the answer is 5, but the exact calculation yields 5.5. **Final answer:** $$5.5$$