Let's solve the inequality -1 < 5 - 2x \(\geq\) 7.

First, we can simplify the inequality to -1 < 5 - 2x and 5 - 2x \(\geq\) 7.

For -1 < 5 - 2x, we can rearrange it to get:

-1 - 5 < -2x

-6 < -2x

3 > x or x < 3

For 5 - 2x \(\geq\) 7, we can rearrange it to get:

5 - 7 \(\geq\) 2x

-2 \(\geq\) 2x

-1 \(\geq\) x or x \(\leq\) -1

So the solution to the inequality is -1 \(\geq\) x < 3.

The integral values of x that satisfy this inequality are -1, 0, 1, 2.