Call the daughter's age x and the woman (5 times older) 5x.
The sum of their ages is 50 so x + 5x = 50
6x = 50
x = 8 and 1/3
1/3 of a year is 4 months.
The daughter is 8 years 4 months old.
Mom is 5*(8 and 1/3) = 41 and 2/3 = 41 years 8 months.
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