I've never heard of the term "city break." Is it a British term? You could just say that, "I went to the city for X days." In American English we don't really have a term for vacations in cities.

City break is a trip taken into the city for pleasure. It could be for a day or two or even more. So your 5-Day trip to London can be termed as city break. As far as using it in a sentence is concerned, just like you use the word break similarly you can use city break also. eg. I'm taking a city break to Rio next weekend.