I have a slight idea on what the attack would be. But my question is: how would one detect if n long messages (n>5) have been encrypted with the same one time pad, K?
Specifically, the $K(K-1)/2$ symbolwise difference of the, say $K$, messages should obey the plaintext distribution. If the plaintext is in a natural language, patterns can be detected using various techniques.
If the messages are binary $n=5$ won't be nearly enough. If the messages are in ASCII, $5$ symbols yield 40 bits, so that might be enough, and you'd even rule out key guesses that don't yield printable ASCII characters when XORed with ciphertext.