David,
The 1880
Limestone Co., AL (Beat 5) has the following census record:
Augustus
Barber 35
Elizabeth 34
Ella 10
Anna 9
Arlenus 8
Henry 7
Sallie 6
Mattie 2
I am not a subscriber to Ancestry.com, so I only have access to their transcribed record.
I believe this to be
Gustavus Henry
Barber who is head of household in the 1870
Giles Co., TN census with wife, Anney and a daughter
Ellin (age 2).