The 1st son was named after the father's father. 
The 2nd son was named after the mother's father. 
The 3rd son was named after the father. 
The 4th son was named after the father's oldest brother. 
The 5th son was named after the father's 2nd oldest brother or mother's  oldest brother. 
The 1st daughter was named after the mother's mother. 
The 2nd daughter was named after the father's mother. 
The 3rd daughter was named after the mother. 
The 4th daughter was named after the mother's oldest sister. 
The 5th daughter is named after the mother's 2nd oldest sister or father's oldest sister. 

English and Welsh Naming Patterns:  1700-1870
First Daughter was named after the Mother's Mother. 
Second Daughter was named after the Mother's Father's Mother. 
Third Daughter was named after the Mother. 
Fourth Daughter was named after the Mother's oldest Sister. 
First Son was named after the Father's Father. 
Second Son was named after the Mother's Mother. 
Third Son was named after the Father. 
Fourth Son was named after the Father's oldest Brother. 
Irish 1800's
First Daughter was named after the Paternal Grandmother 
Second Daughter was named after the Maternal Grandmother 
First Son was named after the Paternal Grandfather 
Second Son was named after the Maternal Grandfather 
Then alternate names using the Grandmother's, Grandfather's, Mother's, Aunt's, and Uncle's names

Scottish 1700 - 1800 and Early Dutch
First Daughter was named for her Maternal Grandmother 
Second Daughter was named for her Paternal Grandmother 
Third Daughter was named after her Mother 
Other Daughters were named after other Family Members 
First Son was named after his Paternal Grandfather (sometimes Maternal) 
Second Son was named after his Maternal Grandfather (sometimes Paternal) 
Third Son was named after his Father

Old German
The first name of each Daughter was usually the first name of the Mother. 
The first name of the Son was usually the first name of the Father.  Often  the middle name of each child was the name of the baby's baptismal sponsor
and they were usually called by his/her middle name.