The five struck a deal with prosecutors to receive five month sentences in exchange for pleading guilty, as another three of their compatriots did in February.
Montenegro's state prosecutor has alleged that the plot included a plan to assassinate then Prime Minister Milo Djukanovic on October 16 in an attempt to take over the government and derail its bid to join NATO.
In a statement, the prosecutor on March 8 said: "Five citizens of Serbia admitted to being part of a criminal organization whose plan was to break into the parliament of Montenegro violently," with the aim of seizing it.
Authorities have accused "Russian nationalists" of orchestrating the alleged plot, saying pro-Moscow Serbs were hired to carry it out.
Montenegrin prosecutors suspect 25 people, mostly Serbian citizens, of links to the alleged coup.
They also have launched a manhunt for two Russians who are on the run.
The suspects include two leading pro-Russia lawmakers from Montenegro's opposition Democratic Front (DF), Andrija Mandic and Milan Knezevic.
Their parliamentary immunity was lifted in February so that they could face charges.
Mandic and Knezevic have repeatedly denied being involved in a coup plot.
They claim the allegations of a plot are politically motivated.
They have also denied knowing any of the sentenced Serbs.
Montenegro hopes to join NATO later in 2017.
Russia opposes NATO's further enlargement in the Balkans and says membership for Montenegro would be a "provocation."