40, 40, 31, 31, 22, 22, 13, … choose which pair of numbers comes next?

The answer is $\boxed{\text{C. }4, 13}$.

In this sequence, each number is repeated, then 9 is subtracted to get the next number. So the next pair of numbers is $13 – 9 = 4$, followed by $13$.

Option A is incorrect because $13$ is not followed by $4$.

Option B is incorrect because $13$ is not followed by $5$.

Option C is correct because $13 – 9 = 4$, followed by $13$.

Option D is incorrect because $9$ is not followed by $4$.

Option E is incorrect because $4$ is not followed by $4$.