**Drawing the Points**

To begin, let's draw the three collinear points A, B, and C. We can assume that these points lie on a horizontal line for simplicity. Let's label the points as shown below:

A-----B-----C

**Drawing the Parallel Line**

Next, we need to draw two points D and E such that the line passing through them is parallel to the line passing through A, B, and C. We can place D and E above or below the line ABC. Let's assume D is above the line and E is below the line. Now, we have the following configuration:

D
|
A-----B-----C
|
E

**Drawing Lines through the Points**

Given these points, we need to draw all possible lines passing through A, B, C, D, and E. Let's examine the different scenarios:

1. Line through A, B, and C: This line is already drawn and represents the given collinear points A, B, and C.

2. Line through A, B, and D: Since D is above the line ABC and parallel to it, we can draw a line passing through A, B, and D. This line will be parallel to the line ABC.

3. Line through A, B, and E: Similarly, since E is below the line ABC and parallel to it, we can draw a line passing through A, B, and E. This line will also be parallel to the line ABC.

4. Line through A, C, and D: We can draw a line passing through A, C, and D. This line will intersect the line ABC at point D and will be parallel to the line BE.

5. Line through A, C, and E: Similarly, we can draw a line passing through A, C, and E. This line will intersect the line ABC at point E and will be parallel to the line BD.

6. Line through B, C, and D: We can draw a line passing through B, C, and D. This line will intersect the line ABC at point D and will be parallel to the line AE.

7. Line through B, C, and E: Similarly, we can draw a line passing through B, C, and E. This line will intersect the line ABC at point E and will be parallel to the line AD.

**Total Number of Lines**

In total, we can draw 7 lines passing through the given points A, B, C, D, and E. These lines are:

1. Line through A, B, and C
2. Line through A, B, and D
3. Line through A, B, and E
4. Line through A, C, and D
5. Line through A, C, and E
6. Line through B, C, and D
7. Line through B, C, and E

Therefore, there are a total of 7 lines that can be drawn through the given points.