Well air conditioners are set to keep houses at a certain temperature. If the five minutes of darkness will have a measurable affect on temperature then air conditioners won't have to work as hard to keep houses cool.
The partial eclipse will last about 2.5 hours. I don't know how much air conditioning would be impacted, but it's not just the totality at work.
In a very near total solar eclipse in I believe the summer of 1991, it was a blistering hot day in Arizona and during the eclipse the temperature dropped substantially. I don't know the numbers, but I remember being surprised at how nice and comfortable the temperature drop was, which lasted for much longer than 5 minutes.
How much of a lag was there between the eclipse itself and the drop in temperature? Even if the drop is immediate I don't expect the thermostats to turn off right away, as it will take some time for the cold to migrate into buildings.