If Morpheus found 5 previous "The Ones", then I believe that there would still need to be 5 separate iterations of Neo, since after each iteration, the Architect wipes out Zion except for a small number of people that are used for repopulation. Morpheus would need to have been part of each of those genocides which he probably would have brought up in conversation.
the matrix could have gone trought 5 iteractions of the one cicle that morpheus knew nothing about, each resulting in the destruction of zion.
yet in this current version of the matrix, during this cicle, morpheus could have find 5 previous individuals that he tough were candidates to being the one, all that were ultimately not the one and who died fighting smith, before finaly finding neo the actual one for this latest cicle of the matrix.
Had the Morpheus 5 been kept in, it would have been trivial to use a different number of cycles (7, 10, 400, whatever) and avoid the confusion.