To solve the inequality \(-1 < 3 - 2x \leq 5\), we will break it down into two separate inequalities:

1. \( -1 < 3 - 2x \)

2. \( 3 - 2x \leq 5 \)

Solve each inequality separately:

1. \( -1 < 3 - 2x \)

Add \(2x\) to both sides:

\( 2x - 1 < 3 \)

Add \(1\) to both sides:

\( 2x < 4 \)

Divide by \(2\):

\( x < 2 \)

2. \( 3 - 2x \leq 5 \)

Subtract \(3\) from both sides:

\( -2x \leq 2 \)

Divide by \(-2\) (remember to reverse the inequality when dividing by a negative number):

\( x \geq -1 \)

Now, combine the solutions from both inequalities:

\( -1 \leq x < 2 \)

This means the integer values of \(x\) that satisfy the original inequality are -1, 0, and 1.