A. The house is quite old and in a bad shape.
B. Through it, I can see an old woman seated in a chair.
C. Far away in a narrow street there is a house.
D. Her face is worn and full of wrinkles.
E. One of the windows is open.

The nouns used in the passage are house-woman-street-face-windows. 

We can sequentially arrange these nouns as: There is a street, where there is a house, which has windows, through which there is a woman with a face. 

This is the sequential arrangement of nouns that make sense. Let us try arranging the 5 sentences in a way that make sense, while arranging the nouns sequentially. 

C. Far away in a narrow street there is a house.
A. The house is quite old and in a bad shape.
E. One of the windows is open.
B. Through it, I can see an old woman seated in a chair.
D. Her face is worn and full of wrinkles.

Hence, the correct order of sentences is CAEBD