The answer is $\boxed{31}$.
In the sequence $14:9$, the first number is $14$ and the second number is $9$. The difference between these two numbers is $5$. In the sequence $26:x$, the first number is $26$ and the second number is $x$. We want to find a number $x$ such that the difference between $26$ and $x$ is $5$. The only number that satisfies this condition is $31$. Therefore, the answer is $\boxed{31}$.
Here is a brief explanation of each option:
- Option A: $12$. The difference between $14$ and $12$ is $2$, which is not equal to $5$. Therefore, this is not the correct answer.
- Option B: $13$. The difference between $14$ and $13$ is $1$, which is not equal to $5$. Therefore, this is not the correct answer.
- Option C: $31$. The difference between $26$ and $31$ is $5$. Therefore, this is the correct answer.
- Option D: $15$. The difference between $26$ and $15$ is $11$, which is not equal to $5$. Therefore, this is not the correct answer.
