China last week reported its first MERS case, that of a South Korean man who tested positive after breaking a voluntary house quarantine and travelling to Hong Kong and on to mainland China.
South Korea reported its first two deaths from MERS on Tuesday, fuelling fear in the country which has reported the most cases outside the Middle East, where the disease first appeared.
South Korea has quarantined or isolated about 1,300 people for possible MERS infection.
Of the five new cases, four had been in the same hospital as the first patient, a 68-year-old man who had just returned from a trip to four countries in the Middle East. The other, a 60-year-old man, caught it from another infected person.
Media said health authorities were conducting tests on an elderly patient who died on Sunday after sharing the same hospital ward with one of the two MERS-infected people who had died. Officials said it was likely she died of existing illness.
Read MoreAvian flu spread raises some concerns about human infection
More than 200 schools, most in the province of Gyeonggi around the capital, Seoul, and where the first death occurred on Monday, were shut for the week, the Education Ministry said.
The new cases would bring the total number globally to 1,166, based on World Health Organization (WHO) data, with at least 436 related deaths.
The WHO has not recommended trade or travel restrictions for South Korea, although South Korean border control authorities have put a ban on overseas travel for people isolated for possible infection, a health ministry official said.
Pressure is growing for the government to identify the hospitals treating infected patients as fear and confusion mount.
Public health authorities have insisted it was "helpful" to keep the names of the hospitals from the public, but in an opinion poll published on Wednesday 83 percent of respondents demanded that the government identify them.
Ian Jones, a specialist virologist at Britain's University of Reading who has followed MERS since it emerged, said transparency would help in the effort to stop the outbreak.
"Being open about the cases, their locations and their condition, is best for control - even if this causes some alarm in the short term," he said.
Read MoreThe holy grail of treating disease: Intarcia
Some experts have said the 38 percent death rate from MERS might be overstated as patients with little or no symptoms might go undetected. The death rate from SARS was 9 to 12 percent, rising to more than 50 percent for patients over 65.
Symptoms of MERS can include cough, fever and shortness of breath. It can lead to respiratory failure, the WHO said.