Since $p<q$ are odd, it means $p< \frac {p+q} {2} < q$, with $\frac {p+q} {2} = ab$ integer, and moreover, not a prime (sitting between two consecutive primes). Thus $p+q = 2ab$ with $a,b > 1$ (notice that for $(p,q) = (3,5)$ we have $p+q = 2^3$, so all three of the factors may in fact be equal).