Any county in the state may lease any property owned by it to the United States of America or to any agency thereof for a term not exceeding ninety-nine years upon such conditions as may be contained in a written agreement therefor executed on behalf of the county by its board of county commissioners, and by any person on behalf of the United States of America or any agency thereof who has been thereunto authorized: PROVIDED, That any lease made for a longer period than ten years hereunder shall contain provisions requiring the lessee to permit the rentals for every five-year period thereafter, or part thereof, at the commencement of such period, to be readjusted upward and fixed by the board of county commissioners. In the event that the lessee and the board of county commissioners cannot agree upon the rentals for the five-year period, the lessee shall submit to have the disputed rentals for such subsequent period adjusted by arbitration. The lessee shall pick one arbitrator and the board of county commissioners one, and the two so chosen shall select a third. No board of arbitrators shall reduce the rentals below the sum fixed or agreed upon for the last preceding period. All buildings, factories or other improvements made upon property leased under this proviso shall belong to and become property of the county, unless otherwise stipulated, at the expiration of the lease.