The correct answer is E

Explanation

The inequality |X—5|≤2 is equivalent to -2≤X—5≤2. Adding 5 to each term of this inequality gives -2+5≤X—5+5≤2+5, which is equivalent to 3≤X≤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|≤2.