**Problem Analysis**

Let's assume the current ages of the two children are x and y, and the current age of the father is z. We are given two pieces of information:

1. Father's age is three times the sum of the ages of his two children.
z = 3(x + y)

2. After 5 years, the father's age will be twice the sum of the ages of his two children.
z + 5 = 2((x + 5) + (y + 5))

**Solving the Equations**

To solve the above equations, we need to find the values of x, y, and z.

1. Rewrite the first equation in terms of z:
z = 3x + 3y

2. Substitute the value of z from equation 1 into equation 2:
3x + 3y + 5 = 2(x + 5 + y + 5)

3. Simplify the equation:
3x + 3y + 5 = 2x + 2y + 20

4. Combine like terms:
x + y = 15

**Finding the Age of the Father**

Now that we have the equation x + y = 15, we can substitute this value back into equation 1 to find the age of the father.

1. Substitute x + y = 15 into equation 1:
z = 3(15)
z = 45

Therefore, the age of the father is 45 years.

**Verification**

To verify our solution, we can check if the given conditions are satisfied:

1. Father's age is three times the sum of the ages of his two children:
45 = 3(15) - This condition is satisfied.

2. After 5 years, the father's age will be twice the sum of the ages of his two children:
45 + 5 = 2((15 + 5) + (15 + 5))
50 = 2(40) - This condition is also satisfied.

Hence, our solution is correct.

**Final Answer**

The age of the father is 45 years.