AbstractLet ℒ︁k(3 ≦k<ℵ0) denote the lattice of clones of finitary operations on ak‐element set. One interesting characteristic of the uncountable lattice ℒ︁kis the minimumlkof the cardinalities of maximal chains in ℒ︁k. It is known that forkprimelk= 5. In this paper the 5‐element maximal chains contained in ℒ︁kare investigated. It is proved that forkcompositelk≧ 6 while forkprime there are exactly (k–2)! (k+ 4) 5‐element maximal chains in ℒ︁k, each clo