[One solution to this problem is given here so that the students understand the concept. The students may attempt to construct another problem based on the same conditions.]

Solution:
One root of this quadratic equation is 5.
Then the other root can be any real number (positive, negative, zero).
Let’s take the other root as 2.

Now, we can construct the problem as follows:

Smita is 3 years younger than her sister Mita. (5 − 2 = 3)
The product of their ages is 10. (5 × 2 = 10)
Find their ages. [1 Mark]

Let, Mita’s age be x years.
∴ Smita’s age = x − 3 years. [1 Mark]

From the given information,
x(x − 3) = 10
∴ x² − 3x = 10
∴ x² − 3x − 10 = 0 [1 Mark]