The Problem:
There is a series of 5 consecutive integers. The average of the first three numbers is represented by 'n'. We need to find the average of all five numbers.

Understanding the Problem:
To solve this problem, we first need to understand the concept of consecutive integers. Consecutive integers are numbers that follow each other in order without skipping any numbers. For example, 1, 2, 3, 4, and 5 are consecutive integers.

Formulating the Solution:
Let's assume the first number in the series is 'x'. Since the numbers are consecutive, the next four numbers will be (x+1), (x+2), (x+3), and (x+4).

Finding the Average of the First Three Numbers:
According to the problem statement, the average of the first three numbers is 'n'. Therefore, we can write the equation as:
(x + (x+1) + (x+2))/3 = n

Simplifying the equation, we get:
(3x + 3)/3 = n
3x + 3 = 3n
3x = 3n - 3
x = (3n - 3)/3
x = n - 1

Finding the Average of all Five Numbers:
Now that we have the value of the first number, we can find the average of all five numbers. Let's add up all the numbers in the series and divide it by 5:
(x + (x+1) + (x+2) + (x+3) + (x+4))/5

Substituting the value of 'x' in terms of 'n', we get:
((n-1) + (n-1+1) + (n-1+2) + (n-1+3) + (n-1+4))/5
(n-1 + n + n+1 + n+2 + n+3 + n+4)/5
(5n + 9)/5
5n/5 + 9/5
n + 9/5

Therefore, the average of all five numbers is represented by n + 9/5.

Conclusion:
In conclusion, the average of the five consecutive integers is n + 9/5. This can be derived by finding the average of the first three numbers using the given information and then finding the average of all five numbers by considering the consecutive nature of the series.