Well, I don't know if this is the seven-word summary you're looking for, but here is one summary statement of those five chapters: Jem and Scout break through some stereotypes.
Before this summer, Jem and Scout have been fairly well insulated from some of the world's harsher realities. They see different classes and different races of people, but they have not really had to see some of the ugliness that happens when people start acting on their prejudices and their ignorances. In each of these chapters, the kids learn some new reality about living in this time and place.
Chapter 11 is a revelation to Jem, especially, about stereotypes and courage. He realizes Mrs. DuBose is not just a mean, cranky old woman; instead he sees her courage as she weans herself from morphine even though she has no need to do so.
Chapter 12 is eye-opening for both kids, as they attend church with Calpurnia. They've assumed all black people are like Cal and can read; instead, their eyes are opened to the truth and the beauty of "linin'." They encounter a rude, low-class black woman, as well--a reminder that boorish behavior is not specific to race.
Chapter 13 is trouble for both kids, but primarily for Scout, as Aunt Alexandra has come to town with the intention of turning her into a stereotypical "lady." For both of them, this is a term associated with corsets and teas and being "proper." Aunt Alexandra tries to instill upon both kids the importance of 'family' and 'heritage,' but her efforts fall flat. Atticus finally tells them to ignore the whole thing--the concept of the stereotypical family legacy, tradition, and heritage is not the only important thing about who a person is.
Chapter 14 represents a change in the relationship between the siblings. Until now, Jem had been the stereotypical defacto "boss of her." In this chapter, Scout has come of age and now only has to obey her older brother if he can make her do so.
In chapter 15, Scout and Jem (and now Dill) are faced with the ignorance of blind prejudice. They're too naive to see what the gathering at the jail was really about, but Scout broke through by treating this clan of Cumminghams as if they were neighbors and friends. This is the very attitude which diffuses the potentially violent scene.
These are pivitol "coming of age" chapters for them both as they are faced with diverse stereotypes, and it is much needed as they prepare to face what's ahead of them in the days and weeks to come.