To solve the problem, we'll follow these steps:
1. Substitute the given values for \( x \) and \( y \):
- We are given \( x = 3 \) and \( y = 6 \).
2. Calculate the sum of \( x \) and \( y \):
[tex]\[
x + y = 3 + 6 = 9
\][/tex]
3. Substitute this sum into the expression:
[tex]\[
-5 - (x + y) = -5 - 9
\][/tex]
4. Perform the subtraction inside the parentheses:
[tex]\[
-5 - 9 = -14
\][/tex]
5. Divide the result by 2:
[tex]\[
\frac{-14}{2} = -7
\][/tex]
6. Check the corresponding option:
[tex]\[
\boxed{-7}
\][/tex]
Thus, the correct answer is [tex]\(\boxed{-7}\)[/tex].
