Whenever the relation of landlord and tenant shall have existed between any persons, the possession of the tenant shall be deemed the possession of the landlord until the expiration of 5 years from the expiration of the tenancy, or, where there has been no written lease, until the expiration of 5 years from the time of the last payment of rent, notwithstanding that such tenant may have acquired another title, or may have claimed to hold adversely to the landlord. But such presumptions shall not be made after the periods herein limited.