The first step in solving this problem is to calculate the area of each face of the box.
The box has six faces (two identical pairs of three different rectangles): one pair is from the box length and box width, another pair is from the box length and box height, and the final pair is from the box width and box height.
Firstly, let's consider the first pair of faces that is formed by the box length and box width. We're given that the length of the box is 10 units, and the width is 7 units. The area of a rectangle is calculated by multiplying its length by its width. Thus, the area of the first pair of faces is 10 * 7, which equals 70 square units.
Next, let's calculate the area of the second pair of faces that is formed by the box length and box height. The length of the box is 10 units, and the height is 5 units. Therefore, the area of the second pair of faces is 10 * 5, which equals 50 square units.
Finally, let's find the area of the final pair of faces, which is formed by the box width and box height. The width of the box is 7 units and the height is 5 units. Hence, the area of the third pair of face is 7 * 5, which equals 35 square units.
Next, we need to calculate the total area of wrapping paper needed. Because each pair of faces appears on the box twice, we need to multiply each of the calculated face areas by two. So, the total area is 2 * (70 + 50 + 35), which amounts to 310 square units.
In conclusion, Daniella would need a minimum of 310 square units of wrapping paper to completely cover the box.