To find the area of the rectangle, we use the formula for the area of a rectangle:
\[ \text{Area} = \text{length} \times \text{height} \]
According to the problem, the height of the rectangle is 5 centimeters, and the length is twice the height:
\[ \text{length} = 2 \times \text{height} = 2 \times 5 = 10 , \text{cm} \]
Now, we can calculate the area:
\[ \text{Area} = \text{length} \times \text{height} = 10 , \text{cm} \times 5 , \text{cm} = 50 , \text{cm}^2 \]
Thus, the area of the rectangle is 50 cm².