Father's current age and the ages of his five children are unknown. Let's assume the father's age is F and the ages of his five children are C1, C2, C3, C4, and C5, respectively.

We can create an equation based on the given information:
F = C1 + C2 + C3 + C4 + C5 -- (Equation 1)

According to the second statement, after 15 years, the father's age will be half of the sum of his children's ages. Let's calculate the sum of the children's ages after 15 years:
(C1 + 15) + (C2 + 15) + (C3 + 15) + (C4 + 15) + (C5 + 15) = 2(F + 15) -- (Equation 2)

Now, let's solve the equations to find the value of F, the father's age.

Solving the equations:

Step 1: Substitute equation 1 into equation 2:
(C1 + 15) + (C2 + 15) + (C3 + 15) + (C4 + 15) + (C5 + 15) = 2(F + 15)
C1 + C2 + C3 + C4 + C5 + 5(15) = 2F + 2(15)
C1 + C2 + C3 + C4 + C5 + 75 = 2F + 30
C1 + C2 + C3 + C4 + C5 = 2F - 45 -- (Equation 3)

Step 2: Substitute equation 3 into equation 1:
F = C1 + C2 + C3 + C4 + C5
F = 2F - 45
F - 2F = -45
-F = -45
F = 45

Hence, the father's age is 45.

Explanation:

The problem can be solved by setting up two equations. The first equation is based on the current ages, where the father's age is equal to the sum of his five children's ages. The second equation is based on the ages after 15 years, where the father's age will be half of the sum of his children's ages.

By solving these equations simultaneously, we can determine the value of the father's age. In this case, the father's age is found to be 45 years.

It is important to carefully analyze the given information, set up the equations, and solve them step by step to find the solution.