Correct Option (D)

To definitively determine the oldest person or persons among A, B, C, D, E, and F, a complete and unambiguous relative age hierarchy must be established. The given statements provide the following relationships:

A is older than B (A > B)
C and D are of the same age (C = D)
E is the youngest (E < all others)
F is younger than D (D > F)
F is older than A (F > A)

By sequentially combining these statements, the complete age order can be constructed:

From statements (4) and (5): D > F > A
Incorporating statement (1): D > F > A > B
Incorporating statement (2): C = D > F > A > B
Incorporating statement (3): C = D > F > A > B > E

This comprehensive sequence, C = D > F > A > B > E, clearly identifies C and D as the oldest individuals. Each of the five statements is indispensable for forming this complete and unambiguous hierarchy:

Statement (1) A > B is crucial for placing B within the overall sequence, ensuring B's age is established relative to A and consequently to C and D. Without it, B's position would be unknown, potentially allowing B to be the oldest.
Statement (2) C = D establishes the equal age of C and D, identifying them as a pair that ultimately occupies the oldest position.
Statement (3) E is the youngest definitively places E at the lowest end of the hierarchy, confirming E is not the oldest.
Statement (4) F < D establishes D's seniority over F, forming a vital link in the chain leading to D as one of the oldest.
Statement (5) F > A establishes F's seniority over A, another critical link that connects A to the higher-ranking individuals.

The omission of any single statement would result in an incomplete or ambiguous age comparison, thereby making it impossible to definitively determine the oldest person(s) among all six individuals. Therefore, all five statements are required.

Incorrect Options:

Options suggesting that only two, three, or four statements are sufficient are incorrect because fewer than five statements would lead to an incomplete or ambiguous age hierarchy. For example:

If statement (1) (A > B) were omitted, the relative age of B would be unknown, meaning B could potentially be older than C or D, thus preventing a definitive determination of the oldest.
If statement (2) (C = D) were omitted, the relationship between C and D would be unknown, making it impossible to determine if one is older than the other or if they are equally old, impacting the identification of the oldest pair.
Similarly, removing any other statement would either break a critical link in the age comparison chain or leave an individual's relative age undefined, thereby precluding a conclusive identification of the oldest person(s) among all six individuals.