Let x be the current age of the daughter. Then, the current age of the woman would be 4x (since the woman is four times as old as her daughter).
In five years, the daughter will be x + 5 years old, and the woman will be 4x + 5 years old.
According to the problem statement, in five years' time, the square of the woman's age will exceed the square of her daughter's age by 120 years:
(4x + 5)^2 - (x + 5)^2 = 120
Expanding the squares, we get:
16x^2 + 40x + 25 - (x^2 + 10x + 25) = 120
Simplifying and solving for x:
15x^2 + 30x - 95 = 0
Using the quadratic formula:
x = (-30 ± sqrt(30^2 - 415(-95))) / (2*15)
x = (-30 ± sqrt(11700)) / 30
x = (-30 ± 108.248) / 30
x = -1.275 or x = 4.275
Since age cannot be negative, the only valid solution is:
x = 4.275
Therefore, the daughter is currently approximately 4.275 years old.