Find the next two numbers in the series 5, 12, 15, 22, 25, 32, _, _.

Concept: In an alternating-addition number series, terms are generated by repeating two different additive steps in a fixed cycle (here, +7 then +3) rather than by a single constant difference.

Application: Applying the cycle step by step from the start of the series:

1. 5 + 7 = 12

2. 12 + 3 = 15

3. 15 + 7 = 22

4. 22 + 3 = 25

5. 25 + 7 = 32

6. 32 + 3 = 35

7. 35 + 7 = 42

So the next two numbers are 35 and 42.

Cross-check: The differences between consecutive terms run 7, 3, 7, 3, 7, 3, 7 - a consistent two-step alternating cycle throughout, confirming that 35 and 42 correctly continue the pattern.