For an adiabatic process, $PV^\gamma = \text{constant}$. For a monoatomic gas, $\gamma = 5/3$. Using the ideal gas law, $V = nRT/P$. Substituting this gives $P(nRT/P)^{5/3} = \text{constant}$, which simplifies to $P^{-2/3} T^{5/3} = \text{constant}$. So, $P \propto T^{5/2}$. Therefore, c = 5/2.