The order was issued late Wednesday night.
The five are Chattrawadi Amornpat, 34, Ekkapop Luara, 22, former PM’s Office minister Jakrapob Penkair, Giles Ungpakorn, and Chupong Thithuan.
Chattrawadi is a hairdresser working in London. She has allegedly posted video clips on a social network site that criticised the monarchy. Her parents have filed complaints against her with the Crime Suppression Division.
Ekkapop is better known as Tung Achiwa. He allegedly criticised the Royal Family at a red shirt rally at the Rajamangkala Stadium in November 2013.
Jakrapob made a speech deemed insulting to the Royal Family on August 29, 2007.
Giles has written a book, “A Coup for the Rich”, which criticises the 2006 power seizure and the Royal Family. He was charged in January 2009 but fled to England.
Chupong was the host of a radio programme with a red-shirt community radio station. He allegedly criticised the Royal Family during his programme. He has fled to the US and has been campaigning against the Royal Family with the US red-shirt group.