Three of the sailors were found and in stable condition, the Navy said Sunday, but the other two were not located.
The crash was not due to any hostile activity, the Navy said, and the incident is under investigation.
The helicopter and Navy warship are part of the USS Nimitz carrier strike group, stationed in the Red Sea as part of the White House's military options for Syria.
Pentagon officials last week extended the deployment of the Nimitz strike group, as well the Navy destroyer USS Barry, in the coastal waters near Syria.
The names of the service members who are presumed dead are being withheld while the families are notified.