According to the average form of Newton's law of cooling: $\frac{T_1 - T_2}{t} = K \left( \frac{T_1 + T_2}{2} - T_s \right)$ where $T_s$ is the temperature of the surroundings.

For the first $5\text{ minutes}$: $\frac{70 - 60}{5} = K \left( \frac{70 + 60}{2} - T_s \right)$ $2 = K(65 - T_s)$ ... (i)

For the next $5\text{ minutes}$: $\frac{60 - 54}{5} = K \left( \frac{60 + 54}{2} - T_s \right)$ $1.2 = K(57 - T_s)$ ... (ii)

Dividing equation (i) by (ii): $\frac{2}{1.2} = \frac{65 - T_s}{57 - T_s}$ $\frac{5}{3} = \frac{65 - T_s}{57 - T_s}$ $5(57 - T_s) = 3(65 - T_s)$ $285 - 5T_s = 195 - 3T_s$ $2T_s = 90$ $T_s = 45^{\circ}\text{C}$

Therefore, the temperature of the surroundings is $45^{\circ}\text{C}$.