The Mi-8 transporter was brought down by rebels, Russia says, in northern Idlib province.
It was returning from delivering humanitarian aid to the besieged city of Aleppo, the defence ministry said.
It is not clear which group brought the helicopter down.
An alliance of forces, including hardline jihadist factions, is the dominant power in Idlib.
Jabhat Fateh al-Sham - formerly known as Jabhat al-Nusra - is among those active in the province, and so-called Islamic State has vowed to carry out jihad against Russian forces.
The helicopter was carrying three crew and two officers.
Pictures on social media, purportedly of the latest Russian helicopter downing, showed burning wreckage and bodies, with armed men milling around.
Footage showed at least one body being dragged away. Another is seen apparently being trampled on.
This is the worst single loss of life for Russia since it launched its air offensive in Syria in support of President Assad towards the end of last year.
Moscow says the helicopter was not involved in a military mission, but was delivering humanitarian aid.  Rebel sources appear to confirm this.  It may not have been known to those who shot the helicopter down, as most of Russia's airpower in Syria has been used for military purposes to support pro-government forces.
But it will further inflame feelings in Russia against rebels in Syria.  Moscow has repeatedly said it sees little distinction between the rebels in terms of brutality and extremism.  The graphic images of victims posted online of the aftermath of the incident will add fuel to the fire.
Russia has previously, though seldom, lost aircraft since it launched operations in support of the Syrian government at the end of September 2015.
In July, two Russian pilots were killed when their helicopter was shot down east of the city of Palmyra by so-called Islamic State (IS).
Last November, the pilot of a Russian Su-24 fighter plane was killed when the aircraft was shot down by Turkey on its border with Syria.
A Russian marine sent on a mission to rescue the pilot was also killed when his helicopter was shot down.
Russia is a key backer of Syrian President Bashar al-Assad and is supporting pro-government forces with air strikes on rebels.
Government forces cut off rebel-held eastern parts of Aleppo last month.
Russia and Syria announced the opening of what they called humanitarian corridors for civilians and rebels wanting to surrender, but few people are reported to have used them, fearing they would be targeted.
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Opposition activists have dismissed as a lie Russian claims that 160 civilians had left rebel-held districts.
The United Nations has warned that basic supplies for the around a quarter of a million people who live in besieged areas will last only three weeks.
On Sunday, rebel groups south of Aleppo launched a push to try to break the siege, in what observers said was one of the biggest counter-offensives in months.
A Russian military helicopter has been shot down in Syria killing all five on board - the deadliest single incident for Russia's military since its air campaign began last September.