(CNN) A second person has died in Washington state and five more people have tested positive with the novel coronavirus, health officials said Sunday.

Four of the new cases, including the second death, are among residents of a long-term nursing facility where officials have been investigating a possible outbreak of coronavirus.

The second death was a man in his 70s who died Saturday, Seattle & King County Public Health said in a release.

A fifth case was reported in Snohomish County, the county's health department said in a release. The five new cases are presumptive, meaning they have been tested positive by a public health lab and are pending confirmation by the Centers for Disease Control and Prevention.

In all, 13 people have tested positive for the novel coronavirus in the state, including a man whose death was reported Saturday , making him the first coronavirus fatality in the United States.

Dr. Jeff Duchin, a health officer with King County, addresses a news conference on Saturday, February 29, 2020, in Seattle.

The 13th case reported late Sunday is a man in his 40s. He is in critical condition, the health department said.

The other three new cases reported Sunday are a woman in her 80s, a woman in her 90s and a man in his 70s. All have underlying health conditions and are in critical condition.

Two other cases were confirmed by Seattle and King County Public Health officials earlier Sunday. They are both males in their 60s with underlying health conditions. One is "in critical but stable condition" at Valley Medical Center in Renton. The other is in critical condition at Virginia Mason Medical Center, a news release said.

"This number is expected to rise as more people are tested and results confirmed," according to a news release from the health department.

However, the two new coronavirus cases are not linked to the long-term health facility where the other coronavirus cases were identified, Katie Ross, a spokeswoman for Washington Health Department, told CNN.

The other cases are a high school boy, a woman who traveled to South Korea and an unidentified man.

Nursing home case

The cases associated with the Life Care Center, a nursing facility in Kirkland, Washington, include a 40-year-old female health care worker who has no known travel outside the US. She is in satisfactory condition at a local hospital, officials said. The second one, a woman in her 70s, is hospitalized in serious condition.

More than 50 residents and staff from the Life Care Center in Kirkland are experiencing symptoms, and will be tested for coronavirus, said Dr. Jeffrey Duchin, health officer for Seattle and King County.

"In addition, we're aware of a number of individuals associated with the long-term care facility who are reportedly ill with respiratory symptoms or pneumonia, and we're in the process of investigating this situation as an outbreak," Duchin said. "We're in the beginning stages of our investigation."

In a statement, the facility said it's not allowing visits from families, volunteers or vendors, and is also placing admissions on hold for the time being.

"We are now in the process of working with the long-term care facility, with the support of the Centers for Disease Control and Prevention," Duchin said. "And we're in a process of providing support to that facility to care for the infected patients, to protect the uninfected patients, and to provide infection control."

Bonnie Holstad's husband, Ken, is a resident at Life Care Center of Kirkland.

Bonnie Holstad, whose husband Ken is staying at the Life Care Center after a fall caused a broken hip, was outside the facility Sunday, trying to get information about her husband's condition. Her husband, who has Parkinson's disease and dementia, had a cough, and the center was not answering phone calls, Holstad said.

So, she made a sign and stood outside the glass front doors of the facility. "No one at Life Care is answering the phones," the sign read. "He needs to be attended to ... what is his temperature?"

A nurse did go down to check on him, she told CNN, and Holstad was told he doesn't have a fever. He's not being tested for the virus, she said, because he doesn't have all symptoms required for testing.

"I was so angry. How can this be that I have to do this, make a sign and go down there?" Holstad said.

"I'm very worried for my husband," Holstad said. "He's one of the vulnerable people," because of his age and his Parkinson's disease.

"I have real problems with how they're handling the interface with family," she said, remarking it was "sort of like a movie about an epidemic in a little town, and they don't know how to handle the situation."

CNN emailed the Life Care Center on Sunday about Holstad's husband but did not receive a response.

Holstad said when she was there Wednesday, she noticed staff members wearing masks. She was told that was because some residents had colds. On Saturday, when she arrived with sandwiches to have lunch with her husband, there was a sign on the door that visitors weren't allowed. It wasn't until she got home and listened to a voicemail from the center that she knew about the coronavirus there.

It's not just the question of his care, Holstad said, but also the fact that family members aren't given any information on what they should be doing after being in contact with the center's residents. Nine family members had visited her husband this week, she said.

High school boy had flu-like symptoms

The high school boy in Snohomish County became ill with flu-like symptoms last Monday, the student's family said in a statement.

He was tested for the flu, but the tests came back negative, so he returned to Jackson High School on Friday, the county health district said in a blog post.

He stayed on campus about five minutes and went home because the family was notified by health officials that his original sample had been tested for coronavirus and came back presumptive positive, the health district said.

"The family didn't know their son was being tested for COVID-19.... Like most people, they assumed it was the flu. They did all the right things," the health district said.

A staff member blocks the view as a person is taken by a stretcher to a waiting ambulance from a nursing facility where dozens of people are being tested for coronavirus.

The high school was closed over the weekend and will be closed Monday to allow for a thorough cleaning and disinfecting before the students return.

District health officials say they are investigating this case since it suggests that local transmission of COVID-19 is occurring.

"Our team is still in the midst of the investigation, so we do not yet know the possible source of infection," said Dr. Chris Spitters, health officer for the Snohomish Health District.

The Life Care Center in Kirkland, Washington, where several residents and staff will be tested for the novel coronavirus.

Hazen High School in the Seattle suburb of Renton will be closed Monday after a student and parent reported having flu-like symptoms, the school district's superintendent, Damien Pattenaude said in a Facebook post Sunday.

The student hasn't been to school since falling sick Wednesday. Along with the parent, who works in the health care industry, the student is self-quarantined at home.

Both have been tested the virus and are awaiting the results. Custodial staff have been mobilized "to begin thoroughly cleaning and disinfecting Hazen," the post said.

State of emergency in Washington state

Elsewhere, the Lake Washington Institute of Technology will be closed Monday and Tuesday after a nursing faculty member and 16 nursing students were at the Life Care Center late last week, said Dr. Amy Morrison, the institute's president. It's also canceling all large community and college events this week, Morrison said in a statement.

In nearby Redmond, seven medics are being quarantined after possible exposure to the virus and "out of an abundance of caution," the Redmond Police Department tweeted Sunday, without giving details on the possible exposure.

In Kirkland, 25 firefighters and two police officers that responded to calls at the facility have been placed under quarantine out of an abundance of caution, according to a statement on the city of Kirkland's website.

"The first responders under quarantine had responded to calls for various medical complaints at the Life Care Center, one of which resulted in a patient being transferred to Evergreen Hospital," the statement says. "Firefighters are either under home quarantine or are utilizing a Kirkland fire station for quarantine."

Washington Gov. Jay Inslee declared a state of emergency Saturday, directing state agencies to use all resources necessary to respond to the outbreak.

"This will allow us to get the resources we need," Inslee said. "This is a time to take common-sense, proactive measures to ensure the health and safety of those who live in Washington state."

There are now at least 85 confirmed and presumptive positive cases of coronavirus in the United States and two deaths. They include 44 people who were aboard the Diamond Princess cruise ship, three people repatriated from China and 38 cases that occurred in the US, according to the Centers for Disease Control and Prevention.