Five World Prime Minister or Prime Minister of the Five Worlds was the position created in the Corellian system to replace the hated post of governor-general, which had been established by the New Republic and was removed by the Galactic Alliance several years after the Yuuzhan Vong War.
The duties of the office included representing the Corellian system in negotiations with outside representatives, and helping coordinate the finances, resources, and policies of the Five Brothers, each of which had their own Head of State that was appointed separately from the Prime Minister.
The relation of the Prime Minister to the lesser Ministers is ambiguous; Thrackan Sal-Solo, Head of State of Corellia, managed to evict and replace the Minister of War apparently without the current Prime Minister's approval, and the position of the Prime Minister was defined as the head of a "coalition" of politicians, each which wanted to assume the position.
The Prime Minister was addressed as "Your Excellency" or "Minister"/"Madame Minister," and lived in the Prime Minister's Residence.
The first Five World Prime Minister was Aidel Saxan, who had been in office at least a year prior to the start of the Second Galactic Civil War. When she was assassinated in 40 ABY, her ex-husband, Denjax Teppler, was sworn in as interim Prime Minister.
Shortly thereafter he was apparently replaced in favor of Thrackan Sal-Solo, though Sal-Solo soon declared himself President of Five Worlds. When he was assassinated and replaced with Dur Gejjen, the title of Five World Prime Minister was revived.
After Gejjen's death, the position was (at least temporarily) replaced with a triumvirate.
Sadras Koyan later was elected Five Worlds Prime Minister but when he was killed it is unknown who succeeded him.
In Betrayal, it was hinted that Thrackan would attempt to become Five World Prime Minister by killing or toppling Denjax Teppler. But, in Bloodlines, mention is made neither of Teppler nor the Prime Minister position, and he is still listed as being "Head of State". However, he is also called "President" and referred to as the head of the full Corellian government. Presumably this was the result of editing errors as well as due to Bloodlines having been finished before Betrayal. These errors were retconned near the beginning of Tempest when it was stated that Thrackan had declared himself President of Five Worlds in addition to his position as Head of State of Corellia.