Mission: Impossible (1966) : 5x5

Presidente Rojas plans to give a speech to the U.S. Congress while his Chief of Internal Security Ferrar plans a takeover and sends an assassin known only as Plato (and known only to Ferrar) to kill the Presidente before he gives his speech. The IMF must find out who Plato is and thwart the assassination. Ferrar follows Rojas to the U.S. where the IMF fake a plane crash - when Ferrar wakes up he is on an uncharted island colony inhabited by the prisoners from a missing penal ship. Paris pretends to be a double-agent working for Ferrar that the Chief knows of but never met. Paris reveals his plan to escape and convinces Ferrar that Plato plans a double-cross. When the other ""prisoners"" come after them, Ferrar is forced to hold them off so Paris can go off to thwart Plato, whose identity Ferrar reveals. Paris gets the information to the team in Washington just in time to stop the assassination.