A jury at the Moscow city court last week convicted the five of organising and carrying out the shooting of Politkovskaya, a vehement critic of the Kremlin's policies in Chechnya.
The apparent contract killing of the 48-year-old journalist for the liberal Novaya Gazeta newspaper shocked the world and cast a shadow over President Vladimir Putin's second term in office.
Politkovskaya's family and supporters have welcomed the verdicts but said they did not go far enough since the investigators have still failed to identify the mastermind.
It also asked for a maximum sentence for Makhmudov's uncle Lom-Ali Gaitukayev, convicted of recruiting his three nephews to carry out the crime.
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"A crime was committed that was especially dangerous to society and with special audacity," prosecutor Boris Loktionov said, ITAR-TASS news agency reported.
Makhmudov's brothers Dzhabrail and Ibragim should serve shorter sentences of 19 and 15 years respectively, the prosecutor recommended.