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答案：E
解析：
The inequality |x-5| is less than or equal to 2 is equivalent to negative 2 is less than or equal to (x-5) is less than or equal to 2. Adding 5 to each term of this inequality gives (-2+5) is less than or equal to (x-5+5) is less than or equal to (2+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 |x-5| is less than or equal to 2.
