Step 1: Define dimensions in terms of breadth

Let the breadth of the wall be $b$. Given that the height is 5 times its breadth, so $h = 5b$. The length is 8 times its height, so $l = 8 \times 5b = 40b$.

$l = 40b, \quad h = 5b$

Step 2: Set up the volume equation

The volume of a cuboidal wall is given by $V = \text{Length} \times \text{Breadth} \times \text{Height}$. Substituting our expressions: $V = (40b) \times b \times (5b) = 200b^3$.

$V = 200b^3$

Step 3: Solve for breadth in meters

Equating this to the given volume of $12.8 \text{ m}^3$: $200b^3 = 12.8 \implies b^3 = \frac{12.8}{200} = 0.064$. Taking the cube root gives $b = \sqrt[3]{0.064} = 0.4 \text{ meters}$.

$b = 0.4 \text{ m}$

Step 4: Convert breadth to centimeters

Converting $0.4 \text{ meters}$ to centimeters by multiplying by 100: $0.4 \times 100 = 40 \text{ cm}$.

$b = 40 \text{ cm}$