Logical Analysis

The key is to reverse each of the three "wrong" statements to find out what must be true. Let M's age be M and S's age be S.

1. 
   Statement 1 Negated: S's claim "I am not over 40" is wrong. Therefore, the truth is: S > 40.
   


2. 
   Statement 2 Negated: M's claim "I am 38 AND S is at least 5 years older" is wrong. The logical opposite of "(A and B)" is "(not A) or (not B)". Therefore, the truth is: M ≠ 38 OR S < M + 5.
   


3. 
   Statement 3 Negated: S's claim about M, "you are at least 39," is wrong. Therefore, the truth is: M < 39.
   

Conclusion

We must check if only one pair of ages satisfies these three true conditions.

• 
  Test Case 1 (M=37, S=41): This pair satisfies all three true conditions. (S > 40, M < 39, and the "M ≠ 38" part of the OR condition is met).
  


• 
  Test Case 2 (M=36, S=42): This pair also satisfies all three true conditions. (S > 40, M < 39, and the "M ≠ 38" part of the OR condition is met).
  

Since multiple possible solutions exist, a unique answer cannot be found.

Final Answer: The correct option is D. cannot be determined.