答案：E

解析：

The inequality (absolute value of x minus 5) is less than or equal to 2 is equivalent to negative 2 is less than or equal to (x minus 5) is less than or equal to 2. Adding 5 to each term of this inequality gives (negative 2 plus 5) is less than or equal to (x minus 5 plus 5) is less than or equal to (2 plus 5), which is equivalent to 3 is less than or equal to x is less than or equal to 7. There are five integers (3, 4, 5, 6 and 7) that satisfy this inequality, and so there are five integers that satisfy (absolute value of x minus 5) is less than or equal to 2.