To solve the problem, let's denote the number of people in Group A as (A) and Group B as (B).

Step 1: Set up equations based on the conditions

Condition 1: When 5 people move from A to B, B becomes twice A:
(B + 5 = 2(A - 5))

Condition 2: When 5 people move from B to A, A equals B:
(A + 5 = B - 5) → (B = A + 10)

Step 2: Substitute (B = A + 10) into Condition 1

((A + 10) + 5 = 2(A - 5))
(A + 15 = 2A - 10)
(A = 25)

Step 3: Find (B)

(B = A + 10 = 25 + 10 = 35)

Answer: Group A has 25 people, Group B has 35 people.

(\boxed{25}) (for Group A) and (\boxed{35}) (for Group B).

If the question asks for both, the answer is (\boxed{25}) and (\boxed{35}). Assuming it's two separate boxes, but if combined, maybe (\boxed{25 35}) or as per the problem's requirement. Given common setups, the most likely answer is (\boxed{25}) and (\boxed{35}).

But if the problem expects one box (maybe sum?), no—wait the original problem probably asks for each group, so the answer is 25 and 35.

Final answer (assuming two boxes): (\boxed{25}) and (\boxed{35}).

But if only one box is needed (maybe the question was specific), but given the context, let's go with the two values. However, in some cases, it might be written as (\boxed{25}) and (\boxed{35}).

Since the user might expect the two numbers, the answer is 25 and 35.

(\boxed{25})
(\boxed{35})

But if combined, maybe (\boxed{25 35}), but usually separate. So the final answer is Group A: (\boxed{25}), Group B: (\boxed{35}).

(\boxed{25})
(\boxed{35})

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