One mole of an ideal gas expands adiabatically from an initial state ( $T_{\mathrm{A}}, V_0$ ) to final state ( $T_{\mathrm{f}}, 5 V_0$ ). Another mole of the same gas expands isothermally from a different initial state ( $\mathrm{T}_{\mathrm{B}}, \mathrm{V}_0$ ) to the same final state ( $T_{\mathrm{f}}$, $5 V_0$ ). The ratio of the specific heats at constant pressure and constant volume of this ideal gas is $\gamma$. What is the ratio $T_{\mathrm{A}} / T_{\mathrm{B}}$ ?