I think it is more beneficial to, after 01234, depending on how many numbers are correct, to exclude a couple numbers from the second string.
For example, let's say we get a couple correct numbers in that first string. Maybe "2" and "3" are correct but in the wrong place. We will eventually have to hunt down the correct place for them. In order to not waste any guesses, our second string might be "56783". We will know whether or not 9 is correct based on a process of elimination. If we are told only 4 numbers total are correct after that, then we know 9 must also be correct.
