To find the temperature after 5 minutes you will find the rate of change that occurred in the first minute and apply that to the next 5 minutes.
The temp drops 13 degrees (20-7) after 1 minute, so it will drop 13 more minutes the next minute (7-13= -6 degrees) Another 13 the next minute (-6-13=-19), BUT it will not drop below the actual air temp.
The thermometer should be at -15 degrees after 5 minutes.