The answer is $\boxed{5}$.
The missing number is the sum of the two numbers on either side of it. In this case, the two numbers on either side of the missing number are $3$ and $7$. The sum of $3$ and $7$ is $10$. Therefore, the missing number is $5$.
Option A, $0$, is incorrect because $0$ is not the sum of $3$ and $7$.
Option B, $3$, is incorrect because $3$ is one of the numbers on either side of the missing number.
Option C, $5$, is correct because $5$ is the sum of $3$ and $7$.
Option D, $7$, is incorrect because $7$ is one of the numbers on either side of the missing number.