Answer :

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].