First, we need to calculate the current area of the flowerbed. The area of a rectangle is given by the formula:
\[ \text{Area} = \text{length} \times \text{width} \]
For Annie's flowerbed, the dimensions are 7 feet and 5 feet, so:
\[ \text{Current Area} = 7 , \text{ft} \times 5 , \text{ft} = 35 , \text{ft}^2 \]
Next, Annie wants to expand the area by 60%. To find 60% of the current area, we can calculate:
\[ 0.60 \times 35 , \text{ft}^2 = 21 , \text{ft}^2 \]
Thus, the area that will be added to the flowerbed is:
\[ \text{Area to be added} = 21 , \text{ft}^2 \]
Finally, when rounding to the nearest tenth, the answer is:
\[ \boxed{21.0} , \text{ft}^2 \]