Hanna would have been 40 years old in 1905; it in conceivable (pun intended) that she may have had a child around that year.
I checked the online Minnesota Birth Certificates Index found on the Minnesota Historical Society website for children with a mother whose maiden name was ENGEBRETSEN, using the exact spelling. I then searched for these children in census records to determine the name of their mother. Unfortunately, there are very few pre-1900 births in the database:
1904 REITMANN, Lottie, Goodhue County. mother: Ida, born Norway 1873
1904 ENGELSON, Victor, Swift County. mother: Anna, born Norway 1864. Emigrated (per 1910 census) 1885. Her name on the 1900 census was given as Audriana (spelling?), birth date September 1864.
1905 IVERSON, Beatrice, Hennepin County. mother: Probably Anna, born about 1871 Norway, emigrated 1904. [not certain this is the correct mother for this Beatrice IVERSON]
1906, GULLIKSEN, Olive, Marshall County. mother: Anna, born about 1875 Norway, arrived 1882.
1909 HANSON, Mabel, Lyon County (not certain of parentage)
1909 NJOES, Babe, Hennepin County. mother: Amanda, born Minnesota 1890.
I did not search later years or variations of the name of ENGEBRETSEN.