Can we break longest roads in Catan?

One way to break the longest road is by building another longest road in Catan, But if that is not possible you can also break it by building a House/ City in middle of the opponent's road. Following images shows you how to do that.

Let say this is the longest road your opponent built Step-1 Place a road to build your house, place it so that you will split your opponent into smaller pieces which are less then five Step-2 Build your house, this way the longest road of your opponent is broke

Its not always possible to break your opponent's road, for example consider the following case, Where you can't build a house so that you can split the road into smaller than 5

There is no way you can break this road