6.4. Does there exist 5 distinct positive integers, where the product of the 2 largest numbers equals the sum of all 5 numbers?
6.4 does not exist.

Assume there exist such 5 positive integers $a>b>c>d>e$. Then, $b \geqslant 4$.
If $b \geqslant 5$, then we have
$$
a b \geqslant 5 a > a + b + c + d + e,
$$

which contradicts the problem statement.
Therefore, $b=4$.
Thus, $c=3, d=2, e=1$, and $4a = ab = a + b + c + d + e = a + 10$, which simplifies to $3a = 10$, contradicting the fact that $a$ is a positive integer.