Each takht is a seat of authority because of a specific event, and knowing the events explains why the five are not interchangeable.
The Akal Takht at Amritsar was raised by Guru Hargobind in 1606, immediately after the execution of his father Guru Arjan, as a platform of temporal authority facing the Harmandir Sahib across the water. The arrangement states the doctrine of miri and piri, worldly and spiritual authority held together, in built form. It is the senior takht and the place from which edicts binding on the Panth are issued.
Keshgarh Sahib at Anandpur marks the founding of the Khalsa at Baisakhi in 1699, when Guru Gobind Singh called for volunteers willing to give their heads and initiated the first five.
Damdama Sahib at Talwandi Sabo is where Guru Gobind Singh stayed after the campaigns of 1705 and where the definitive recension of the Guru Granth Sahib, the Damdami Bir, was dictated. Its recognition as the fifth takht came later than the others and its standing has been the subject of dispute.
Patna Sahib in Bihar is the birthplace of Guru Gobind Singh, and Hazur Sahib at Nanded in Maharashtra is where he died in 1708 and where he conferred the succession on the Guru Granth Sahib itself, ending the line of human Gurus. Hazur Sahib retains distinctive practices, including forms of ceremonial not followed at Amritsar, and it is administered separately.
The circuit is recognised rather than commanded, and the order in which the five are named is convention. The question of which body speaks for the Panth, and how the jathedars of the takhts relate to one another, remains contested.