To find the area of the rectangle, we use the formula:
\[ \text{Area} = \text{Length} \times \text{Height} \]
Given that the height (which is the same as the rectangle's width) is 5 cm, and the length is twice the height:
\[ \text{Length} = 2 \times \text{Height} = 2 \times 5 \text{ cm} = 10 \text{ cm} \]
Now, we can calculate the area:
\[ \text{Area} = 10 \text{ cm} \times 5 \text{ cm} = 50 \text{ cm}^2 \]
Therefore, the area of the rectangle is 50 cm².