Solution:

Using Newton's law of cooling:

Let \( T_s \) be the temperature of the surroundings, and \( T_1 = 70^\circ \text{C} \), \( T_2 = 60^\circ \text{C} \), \( T_3 = 54^\circ \text{C} \).

The average temperatures in each time interval are:
1. For first 5 minutes: \( \frac{70 + 60}{2} = 65^\circ \text{C} \)
2. For next 5 minutes: \( \frac{60 + 54}{2} = 57^\circ \text{C} \)

According to Newton's law:
\[
\frac{T_1 - T_2}{T_1 - T_s} = \frac{T_2 - T_3}{T_2 - T_s}
\]

Substitute values:
\[
\frac{70 - 60}{65 - T_s} = \frac{60 - 54}{57 - T_s}
\]

Simplifying:
\[
\frac{10}{65 - T_s} = \frac{6}{57 - T_s}
\]

Cross-multiplying and solving for \( T_s \) gives \( T_s = 45^\circ \text{C} \).