13. As shown in the figure, the ratio of the length to the width of a rectangle is 5:3. If the length of the rectangle is reduced by 5 cm, and the width is increased by 3 cm, then the rectangle becomes a square. The area of the original rectangle is $\qquad$ square centimeters.
【Solution】Solution: First, find the length of one part:
$$
\begin{aligned}
& (5+3) \div(5-3) \\
= & 8 \div 2 \\
= & 4 \text { (cm) }
\end{aligned}
$$
$=4$ (cm)
The length is: $4 \times 5=20$ (cm)
The width is: $4 \times 3=12$ (cm)
The original area is:
$$
20 \times 12=240 \text { (square cm); }
$$

Answer: The original area of the rectangle is 240 square cm. Therefore, the answer is: 240.