\(\alpha = \frac{{{T_2}}}{{{T_1} - {T_2}}}\)
where \(T_1\) and \(T_2\) are the temperatures of hot and cold reservoirs \((in\,kelvin)\) respectively.
\(Here,\alpha = 5,{T_2} = - {20^ \circ }C = - 20 + 273\,K = 253\,K\)
\({T_1} = ?\)
\(\therefore \,\,5 = \frac{{253K}}{{{T_1} - 253\,K}}\)
\(5{T_1} - 5\left( {253\,K} \right) = 253\,K\)
\(5{T_1} = 253\,K + 5\left( {253\,K} \right) = 6\left( {253\,K} \right)\)
\({T_1} = \frac{6}{5}\left( {253K} \right) = 303.6\,K = 303.6 - 273\)
\( = {30.6^ \circ }C \approx {31^ \circ }C\)