(In reply to please read
You have ignored the fact that one of the five numbers
is a function of 4 others such that
a)it is uniquely identified as B's number (calculated by B by a
formula known to A)
b) It provides exact information as to which one of 24 combination occured .
I hope my post (PLEASE READ IT) makes it clear.
In any case I hope you will write a simple program and actually perform this trick albeit computer assisted.