Calculating the heat of formation of propane given its enthalpy of combustion
The equation I had earlier in my first method was wrong. Using Hess's law, we know the change in enthalpy of combustion to be $\pu{-2201.1 kJ/mol}$. Thus:

$$\Delta H^\circ_\text{rxn}=-22201.1 = [3(−393.5) + 4(−285.3)] − [5(0) + x]$$

where $x$ is the heat of formation of propane.

Solving the equation, we get $x = \pu{-101.6 kJ/mol}$.