The given problem requires us to represent the ages of two girls graphically. Let's break down the solution into different steps:

Step 1: Understanding the problem
We are given two girls, and their ages are in the ratio of 5:7. Let's assume the ages of the two girls are 5x and 7x, respectively.

Step 2: Establishing the equation
Eight years ago, their ages were in the ratio of 7:13. We can calculate their ages 8 years ago as (5x - 8) and (7x - 8), respectively. Using this information, we can establish the following equation:

(5x - 8) / (7x - 8) = 7 / 13

Step 3: Solving the equation
To solve the equation, we can cross-multiply:

13(5x - 8) = 7(7x - 8)

Simplifying the equation:

65x - 104 = 49x - 56

16x = 48

x = 3

Step 4: Calculating ages
Now that we have the value of x, we can calculate the ages of the two girls:

Age of the first girl = 5x = 5 * 3 = 15
Age of the second girl = 7x = 7 * 3 = 21

Step 5: Graphical representation
To represent this situation graphically, we can use a bar graph. The horizontal axis represents the girls' ages, and the vertical axis represents the frequency or number of girls.

Graphical representation:
1. Draw a horizontal axis and label it "Age".
2. Mark the age of the first girl (15) on the x-axis and draw a bar above it.
3. Mark the age of the second girl (21) on the x-axis and draw a bar above it.
4. Label the bars as "Girl 1" and "Girl 2" respectively.

This graphical representation will visually depict the ages of the two girls, with the length of the bars representing their ages. The bar for Girl 2 will be longer than the bar for Girl 1 since their ages are in the ratio of 5:7.

Note: It's important to follow the HTML bullet point and heading tags format while presenting the solution in a visually appealing manner.