Given information:
- 5 years ago, the average age of a family of 3 members was 19 years.
- A baby has been born, and the average age of the family remains the same today.
- We need to determine the age of the baby after 8 years.

Let's solve this step by step:

Step 1: Determine the total age of the family 5 years ago.
The average age of the family 5 years ago was 19 years. Since there were 3 members in the family, the total age of the family 5 years ago would be 19 * 3 = 57 years.

Step 2: Determine the total age of the family today.
Since the average age of the family remains the same today, we can conclude that the total age of the family is still 57 years.

Step 3: Determine the current age of the baby.
Let's assume the baby's age 5 years ago was x.
So, the sum of the ages of the other two family members 5 years ago would be 57 - x.

Now, let's consider the current scenario. The baby has aged 5 years, and the other two family members have also aged 5 years. So, the current age of the baby is x + 5, and the current sum of the ages of the other two family members is 57 - x + 5.

Step 4: Formulate the equation.
Since the average age of the family remains the same today, the total age of the family today divided by the number of family members should still be 19. Therefore, we can write the equation as:
(57 - x + 5 + x + 5) / 4 = 19

Simplifying the equation:
(57 + 10) / 4 = 19
67 / 4 = 19
16.75 = 19

Since the equation is not true, this means our assumption of x = baby's age 5 years ago is incorrect.

Step 5: Correct the assumption and solve the equation.
Let's assume the baby's age 5 years ago was y.
So, the sum of the ages of the other two family members 5 years ago would be 57 - y.

Now, considering the current scenario, the baby's age is y + 5, and the sum of the ages of the other two family members is 57 - y + 5.

Reformulating the equation:
(57 - y + 5 + y + 5) / 4 = 19

Simplifying the equation:
(57 + 10) / 4 = 19
67 / 4 = 19
16.75 = 19

Again, the equation is not true. This means our assumption of y = baby's age 5 years ago is also incorrect.

Step 6: Correct the assumption and solve the equation.
Let's assume the baby's age 5 years ago was z.
So, the sum of the ages of the other two family members 5 years ago would be 57 - z.

Now, considering the current scenario, the baby's age is z + 5, and the sum of the ages of the other two family members is 57 - z + 5.

Reformulating the equation:
(57 - z + 5 + z + 5) / 4 =