"We have been collecting details on the missing people from the district offices, and revised the data after verification," disaster authority spokeswoman Shanti Mahat told AFP.
The figure rose from 5,179 reported a day earlier.
The number of bodies retrieved stands at 1,403 bodies, 105 of which had been identified, according to the disaster agency.
Across the border in China, the toll is 43 dead and 519 missing, according to state media.
The combined toll from the deadly glacial mountain collapse on the Nepal-China border from both nations now stands at 1,446 people dead and at least 6,669 missing.
Several hundred foreigners, including tourists and pilgrims, are among the missing.
The sheer scale of the flood was unlike anything witnesses had seen before, with the Nepali government pointing the finger at the dire impact of rising global temperatures on the Himalayan mountains.
Nepal, a largely rural nation of 30 million people, contributes a fraction of global greenhouse gas emissions compared to industrialised nations.
Prime Minister Balendra Shah will take his first foreign trip as leader to address the UN General Assembly on the urgent issue next week.
Nepal estimates the reconstruction bill after the deadly floods will amount to $4.78 billion.