1. **State the problem:** We are given the function $$h(x) = - \frac{2}{3} x - 5$$ and need to find the value of its inverse function at 1, i.e., $$h^{-1}(1)$$. 2. **Recall the definition of inverse function:** The inverse function $$h^{-1}(y)$$ satisfies $$h(h^{-1}(y)) = y$$. To find $$h^{-1}(1)$$, we need to find the value of $$x$$ such that $$h(x) = 1$$. 3. **Set up the equation:** $$ - \frac{2}{3} x - 5 = 1 $$ 4. **Solve for $$x$$:** Add 5 to both sides: $$ - \frac{2}{3} x - 5 + 5 = 1 + 5 $$ $$ - \frac{2}{3} x = 6 $$ 5. **Divide both sides by $$- \frac{2}{3}$$:** $$ x = \frac{6}{- \frac{2}{3}} = 6 \times \frac{3}{-2} = \cancel{6} \times \frac{3}{\cancel{-2}} \times -1 = -9 $$ 6. **Interpretation:** The value of $$x$$ that satisfies $$h(x) = 1$$ is $$-9$$, so $$h^{-1}(1) = -9$$. **Final answer:** $$\boxed{-9}$$