We are given the following information:

• The length of the rectangle is 6 centimeters less than 5 times its width.
• The perimeter of the rectangle is 60 cm.

Let the width of the rectangle be $w$ cm. Then the length of the rectangle is:

$l = 5w - 6 \, \text{cm}$

The formula for the perimeter $P$ of a rectangle is:

$P = 2(l + w)$

Substitute the given perimeter and the expression for the length into the formula:

$60 = 2((5w - 6) + w)$

Simplifying:

$60 = 2(6w - 6)$

$60 = 12w - 12$

Add 12 to both sides:

$72 = 12w$

Now, divide by 12:

$w = 6$

Now that we have the width, we can find the length:

$l = 5(6) - 6 = 30 - 6 = 24$

So, the dimensions of the rectangle are:

$\text{Width} = 6 \, \text{cm}, \, \text{Length} = 24 \, \text{cm}$

In the required format, the answer is $6 \times 24$.

Would you like further clarification on any part? Here are some related questions to explore:

1. How would the dimensions change if the perimeter increased by 10 cm?
2. What if the length was instead 8 cm less than 5 times the width?
3. How can you find the area of the rectangle with these dimensions?
4. Can you solve a similar problem where the relationship between length and width is different?
5. What are other methods to calculate the dimensions of a rectangle given its perimeter and length-width relationship?

Tip: Always start by defining your variables and setting up the correct equation based on the given information.