Britain-based monitor the Syrian Observatory for Human Rights, which gathers information from a large network of sources on the ground, confirmed the death toll.
It also said a large number of people were critically wounded.
SANA said the five were killed and 36 wounded in "Ath-Thawra Street in central Damascus by a rocket fired by terrorists in the Jubar sector", a city suburb.
It also reported one wounded when a rocket hit Baghdad Street, while five rockets that hit the Bab Touma area caused only damage.
Rebel groups took the strategic Jubar district in summer 2013, and loyalist forces began an offensive aimed at retaking it last September.
Residential districts of Damascus come under regular rebel rocket attack, while rebel-held sectors are often the target of regime air raids and artillery bombardment.
On June 17, rockets fired by rebels at central Damascus killed nine people, and on June 28 four people died in a similar attack on the city centre.
According to a toll compiled by the Observatory, the Syria conflict has killed more than 240,000 people.
It was triggered in March 2011 by the bloody repression of peaceful anti-government protests and degenerated into armed revolt and a bloody and devastating civil war.
Regime forces, rebel groups, Kurdish fighters and jihadists are now competing over more and more fragmented territory.
More than half the country's population has been displaced or become refugees.
Last month, United Nations aid chief Stephen O'Brien said more than one million people have been displaced so far this year, many for a second or third time, on top of 7.6 million displaced inside Syria by the end of 2014.
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It also said a large number of people were critically wounded.
SANA said the five were killed and 36 wounded in "Ath-Thawra Street in central Damascus by a rocket fired by terrorists in the Jubar sector", a city suburb.
It also reported one wounded when a rocket hit Baghdad Street, while five rockets that hit the Bab Touma area caused only damage.
Rebel groups took the strategic Jubar district in summer 2013, and loyalist forces began an offensive aimed at retaking it last September.
Residential districts of Damascus come under regular rebel rocket attack, while rebel-held sectors are often the target of regime air raids and artillery bombardment.
On June 17, rockets fired by rebels at central Damascus killed nine people, and on June 28 four people died in a similar attack on the city centre.
According to a toll compiled by the Observatory, the Syria conflict has killed more than 240,000 people.
It was triggered in March 2011 by the bloody repression of peaceful anti-government protests and degenerated into armed revolt and a bloody and devastating civil war.
Regime forces, rebel groups, Kurdish fighters and jihadists are now competing over more and more fragmented territory.
More than half the country's population has been displaced or become refugees.
Last month, United Nations aid chief Stephen O'Brien said more than one million people have been displaced so far this year, many for a second or third time, on top of 7.6 million displaced inside Syria by the end of 2014.
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