I found this entry in the 1912 Lorain city directory.
Charles H. Frederick, Physician and Surgeon: Proprietor of Fifth Street Hospital.
The hospital address was given as 202 Fifth Street. Dr. Frederick was listed in the 1905 city directory and the 1915/1916 city directory, but no mention was made of the hospital in either of those directories. Apparently the private hospital was a short lived venture. If you would like to look for more information, you might try the Black River Historical Society, at 309 5th St. Lorain, Ohio 44052. Phone (440)245-2563 or Fax (440)245-3591. Good Luck!