Answer
There are a number of possible 5-integer solutions. One of them is:
$-3, -2, -1, 0, 1$
Work Step by Step
RECALL:
$|x| \le a \longrightarrow -a \le x \le a$
Thus,
$|x| \le 3 \longrightarrow -3 \le x \le 3$
Therefore the following integers are solutions of the given inequality:
$-3, -2, -1, 0, 1$