S/S Haakon Adelsteen
REDDigitalarkivet "Ship's List Bergen-New York 1871-1873" shows "passenter lists" for a sailing of the "Haakon Adelsten" (departing?) Bergen 20 Mai 1873. The voyages listed on this site show a (maiden?) voyage leaving Christiania 24 April & arriving New York 15 May in 1873. (Would the return voyage have been accomplished in 5 days, or are these two different ships with similar names?)
BorgeS/S Haakon Adelsteen, Captain Müller sailed from Christiania April 24 with about 190 emigrants for America. The ship arrived New York, May 15. The date you found at Digitalarkivet as May 20, is listed in the column with a headline saying "Date of arrival", so I believe we are talking of the same ship. The date given in that database is actually not necessarily the arrival date, but more likely the date when the passenger list was registered by the customs officier in New York. The information on this site comes from the maritime intelligence telegrams printed in the Norwegian newspapers.