5. C
$p$ and $q$ are both odd numbers, so 2 is a prime factor of $p+q$. We can assume that $\frac{p+q}{2}$ is not a prime number, because $p<\frac{p+q}{2}<q$, and $p, q$ are consecutive primes. Let $m$ be a divisor of $\frac{p+q}{2}$, then $\frac{p+q}{2m}$ is also a divisor of $\frac{p+q}{2}$. On the other hand, when $p=3, 4=5$, $p+q$ has exactly 3 prime factors.
5. $p, q$ are two consecutive prime numbers in the sequence of prime numbers excluding 2, arranged in ascending order. The number of prime factors (not necessarily distinct) of $p+q$ is $m$. Then the minimum value of $m$ is ( ).
A. 1
B. 2
C. 3
1. 4