1. **State the problem:** We are given the equation $$h = \frac{9(v - 273.15)}{5} + 32$$ which converts temperature from kelvins ($v$) to degrees Fahrenheit ($h$). We need to find the kelvin temperature $v$ when the Fahrenheit temperature $h$ is 809.33. 2. **Write down the formula:** $$h = \frac{9(v - 273.15)}{5} + 32$$ 3. **Isolate $v$:** Subtract 32 from both sides: $$h - 32 = \frac{9(v - 273.15)}{5}$$ Multiply both sides by 5: $$5(h - 32) = 9(v - 273.15)$$ Divide both sides by 9: $$\frac{5(h - 32)}{9} = v - 273.15$$ Add 273.15 to both sides: $$v = \frac{5(h - 32)}{9} + 273.15$$ 4. **Substitute $h = 809.33$ and calculate:** $$v = \frac{5(809.33 - 32)}{9} + 273.15$$ Calculate inside the parentheses: $$809.33 - 32 = 777.33$$ Multiply by 5: $$5 \times 777.33 = 3886.65$$ Divide by 9: $$\frac{3886.65}{9} = 431.85$$ Add 273.15: $$431.85 + 273.15 = 705$$ 5. **Final answer:** The temperature in kelvins is $$\boxed{705}$$ kelvins.