USC spokesman Alexei Kravchenko has confirmed this when speaking to RIA Novosti.
"I have information that the contract for five subs has been signed," he said.
Recently, the Russian Defence Ministry and USC were reported to have disagreed over the final delivery contract terms of the new Borey-class submarines.
Russian defence minister Anatoly Serdyukov was earlier reported by the news agency as saying that the ministry and the firm had agreed to resume price talks relating to Borey and Yasen (Project 885) submarines programme by 2015.
However, the country’s trade and industry minister Denis Manturov hinted at the possibility of signing of the contract.
"The president made a considered decision that makes it possible to sign a contract with the Defense Ministry until 2020," he said.
Russian President Vladimir Putin said that his government had funded $156bn of the entire armament procurement budget until 2020, for the new warships and submarines procurement, which is expected to be a priority over the next decade.
As part of a state 2020 rearmament procurement programme, the Russian Navy will receive ten new Borey-class submarines, armed with Bulava ballistic missiles by 2020.
The Borey submarines will replace the ageing Russian Delta III and Typhoon-class vessels and are expected to boost the Russian submarine fleet and form the core of the country’s naval force after 2018.
Under the country’s submarine procurement plan, the navy will also be equipped with ten Graney-class nuclear attack submarines, in addition to 20 diesel-electric submarines and six Varshavyanka-class vessels.