It sounds to me as if someone has rounded-up a heap of Enfield parts and said "lets see what we can make".
It would appear to be a total 'bitsa' that has not seen an amourer for many, many years.

At what stage does a rifle become something else - it would appear that the only 'correct' part is the action.

Photos would help to finalise the thinking, but, a No5 it isn't.