A government source and two diplomatic sources told Reuters, Censor.NET reports.
Moldova, a former Soviet state that has long been the focus of a struggle for influence between Russia and the West, expelled the diplomats on May 29. It did not explain the decision, with Prime Minister Pavel Filip saying only that his government had "good reasons".
According to the sources, who are familiar with the case, the five were ejected because of their alleged activities as undercover officers with the Russian military intelligence agency, the GRU.
They said Moldovan officials believed the Russians were recruiting fighters from Gagauzia, an autonomous southern region home to an ethnic Turkish population that is pro-Russian and opposes closer integration with the European Union.
The Moldovan government source and Chisinau-based diplomatic sources all spoke on condition of anonymity because of the sensitivity of the matter. They did not say how the Russians allegedly recruited the fighters, how many were recruited or the reason for their recruitment.
Reuters could not independently verify the allegations about the activities of the five Russians.
The Russian foreign ministry declined to comment. The Russian defense ministry did not respond to requests for comment.
Asked by Reuters if the five Russians were GRU officers, a spokeswoman for the Moldovan foreign ministry said they were diplomats and declined to comment further.
Moldovan intelligence believes fighters recruited from Gagauzia were first sent to a paramilitary training camp in the Rostov region of southern Russia, according to the sources.
The sources did not identify the camp. Russia has used at least two military camps in Rostov to train volunteers for fighting in eastern Ukraine, according to evidence collected by Reuters and the Russian media.
The three sources said some information about Gagauzians fighting in eastern Ukraine was brought to the attention of Moldovan authorities by Ukraine's state security service, the SBU, which gathers intelligence on people fighting with the separatist insurgency in eastern Ukraine.
With information from the SBU, the Moldovan authorities were able to track, arrest and interrogate Gagauzian fighters returning from the conflict, according to the sources. Some became informers, they added.
The SBU did not respond to a request for comment.