Three people aged from 18 to 60 are now confirmed dead from injuries inflicted during the shootings, British-based group Free Tibet said in a statement.
It did not specify how the other two are believed to have died.
Police last week had opened fire on locals in Kardze, a Tibetan-majority area of China's southwestern Sichuan province, rights groups and US-funded broadcaster Radio Free Asia (RFA) said, citing local sources.
The protests in Kardze were sparked by the arrest of a local leader, reports said.
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The US-based International Campaign for Tibet said one protester had committed suicide in custody.
"This shooting and the subsequent treatment of detainees exposes the reality of China's so-called 'rule of law' in Tibet," the group added.
It also said that China's ethnic minority regions in Tibet and far-western Xinjiang, home to the mainly Muslim Uighurs, have been regularly hit by unrest in recent years.
Beijing says it has brought economic development to poverty-stricken Tibetan areas, while claiming to grant broad religious freedoms.
China heavily restricts local and foreign media from reporting in minority areas, making it very difficult to independently verify such reports of unrest.
At least 120 Tibetans in China have set themselves alight since 2009, according to the tallies kept by Free Tibet and RFA.