The coefficient of performance ($\beta$) of a refrigerator is given by the formula: $\beta = \frac{T_2}{T_1 - T_2}$ where $T_2$ is the absolute temperature of the cold reservoir (freezer) and $T_1$ is the absolute temperature of the hot reservoir (surroundings). Given: $\beta = 5$ $T_2 = -20^\circ\text{C} = 273 - 20 = 253\text{ K}$ Substituting these values into the formula: $5 = \frac{253}{T_1 - 253}$ $5(T_1 - 253) = 253$ $5T_1 - 1265 = 253$ $5T_1 = 1518$ $T_1 = \frac{1518}{5} = 303.6\text{ K}$ Converting $T_1$ back to Celsius: $T_1 (^\circ\text{C}) = 303.6 - 273 = 30.6^\circ\text{C} \approx 31^\circ\text{C}$ Therefore, the temperature of the surroundings is nearly $31^\circ\text{C}$.