When the relation of landlord and tenant has existed between any persons, the possession of the tenant is deemed the possession of the landlord until the expiration of five years from the termination of the tenancy, or, where there has been no written lease, until the expiration of five 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 his landlord. But such presumptions cannot be made after the periods herein limited.