Answer :
To find the value of the function at $x = -5$, substitute $-5$ into the polynomial function
$$
f(x) = x^2 - 2x - 7.
$$
Step 1: Substitute $x = -5$ into the function:
$$
f(-5) = (-5)^2 - 2(-5) - 7.
$$
Step 2: Calculate the square term:
$$
(-5)^2 = 25.
$$
Step 3: Evaluate the linear term:
$$
-2(-5) = 10.
$$
Step 4: Combine the constant term along with the results:
$$
f(-5) = 25 + 10 - 7.
$$
Step 5: Sum the numbers:
$$
25 + 10 = 35, \quad \text{and} \quad 35 - 7 = 28.
$$
Thus,
$$
f(-5) = 28.
$$
The final answer is $\boxed{28}$.
$$
f(x) = x^2 - 2x - 7.
$$
Step 1: Substitute $x = -5$ into the function:
$$
f(-5) = (-5)^2 - 2(-5) - 7.
$$
Step 2: Calculate the square term:
$$
(-5)^2 = 25.
$$
Step 3: Evaluate the linear term:
$$
-2(-5) = 10.
$$
Step 4: Combine the constant term along with the results:
$$
f(-5) = 25 + 10 - 7.
$$
Step 5: Sum the numbers:
$$
25 + 10 = 35, \quad \text{and} \quad 35 - 7 = 28.
$$
Thus,
$$
f(-5) = 28.
$$
The final answer is $\boxed{28}$.
