Given that $5 \leq f(x) \leq 8$ for $-7 \leq x \leq 5$, use property 8 of Section 5.2 of the Stewart Essential Calculus textbook to estimate the value of $\int_{-7}^{5} f(x) d x$
\[
\leq \int_{-7}^{5} f(x) d x \leq \square
\]

Step 1 ：The problem provides that the function \(f(x)\) is bounded between 5 and 8 for the interval \([-7, 5]\).

Step 2 ：According to property 8 of Section 5.2 of the Stewart Essential Calculus textbook, the integral of a function over an interval \([a, b]\) is less than or equal to \((b - a)\) times the maximum value of the function on the interval, and greater than or equal to \((b - a)\) times the minimum value of the function on the interval.

Step 3 ：In this case, the interval is \([-7, 5]\), the minimum value of the function is 5, and the maximum value of the function is 8.

Step 4 ：Using these values, we can estimate the integral. The lower bound of the integral is \((5) * (5 - (-7)) = 60\) and the upper bound is \((8) * (5 - (-7)) = 96\).

Step 5 ：Therefore, the integral of the function \(f(x)\) from -7 to 5 is estimated to be between 60 and 96.

Step 6 ：Final Answer: The estimated value of the integral \(\int_{-7}^{5} f(x) d x\) is between \(\boxed{60}\) and \(\boxed{96}\).