Sure, let's break this problem down step by step. We know that the sides of the rectangle are in the ratio of 5:3 and the perimeter of the rectangle is 32 cm.
1. First, let's denote the common ratio as 'x'. Hence, the length of the rectangle becomes 5x and the width becomes 3x.
2. Now, we know that the perimeter of a rectangle is calculated as 2*(length + width). Applying this formula with our variables, it becomes 2*(5x + 3x) = 32 cm.
3. When we simplify the expression inside the brackets, we arrive at 2*(8x) = 32 cm.
4. When we solve for 'x', we cross multiply and divide by 2*8 (16). 'x' will equate to 32/16.
5. Thus, 'x' equals to 2.0.
6. Now, remember that the length is 5x and the width is 3x. We can substitute the 'x' we have found into these expressions to get the actual dimensions of the rectangle.
7. So, the length of the rectangle will be 5*2 = 10 cm and the width of the rectangle will be 3*2 = 6 cm.
So, the dimensions of the rectangle are
Answer: 10 cm by 6 cm.