The length of a rectangle is 23 centimeters less than five times its width. Its area is 42 square centimeters. Find the dimensions of the rectangle.

Step 1 ：Let's denote the width of the rectangle as \(w\) and the length as \(l\). According to the problem, we have two equations:

Step 2 ：\[l = 5w - 23\]

Step 3 ：\[lw = 42\]

Step 4 ：We can substitute the first equation into the second to solve for \(w\), and then substitute \(w\) back into the first equation to find \(l\).

Step 5 ：Solving these equations gives us two possible solutions for \(w\): \(-\frac{7}{5}\) and \(6\).

Step 6 ：However, the width of a rectangle cannot be negative, so we discard the negative solution and take \(w = 6\) as the correct solution.

Step 7 ：Substituting \(w = 6\) back into the first equation, we find that \(l = 5*6 - 23 = 7\).

Step 8 ：\[\boxed{\text{Final Answer: The width of the rectangle is 6 cm and the length is 7 cm.}}\]