Given Information:
- Two circles with radii 5 cm and 3 cm.
- The distance between their centers is 4 cm.

Objective:
- To find the length of the common chord.

Approach:
1. Calculate the distance between the centers of the circles.
2. Determine the position of the centers of the circles.
3. Draw a line segment connecting the centers of the circles.
4. Determine the distance between the centers of the circles.
5. Use the Pythagorean theorem to find the length of the common chord.

Step by Step Solution:

Step 1: Calculate the distance between the centers of the circles.
- Given: The distance between the centers of the circles is 4 cm.

Step 2: Determine the position of the centers of the circles.
- Let the centers of the circles be A and B.
- Let the radius of the larger circle be r1 = 5 cm.
- Let the radius of the smaller circle be r2 = 3 cm.
- Let the distance between the centers of the circles be d = 4 cm.

Step 3: Draw a line segment connecting the centers of the circles.
- Draw a line segment AB with length d = 4 cm connecting the centers A and B of the circles.

Step 4: Determine the distance between the centers of the circles.
- The distance between the centers of the circles is the length of the line segment AB, which is 4 cm.

Step 5: Use the Pythagorean theorem to find the length of the common chord.
- The length of the common chord can be found using the formula:
Length of common chord = 2 * √(r1^2 - (d/2)^2)
where r1 is the radius of the larger circle and d is the distance between the centers of the circles.
- Substituting the given values, we have:
Length of common chord = 2 * √(5^2 - (4/2)^2)
= 2 * √(25 - 4)
= 2 * √(21)
≈ 2 * 4.5826
≈ 9.1652 cm

Answer:
The length of the common chord between the two circles is approximately 9.1652 cm.