The area of a square is calculated using the formula:
\[ \text{Area} = \text{side length}^2 \]
In this case, the side length of the original square is 5 units. Therefore, the area of the original square is:
\[ \text{Area} = 5^2 = 25 \text{ square units} \]
When the square is translated 7 units to the left and 10 units up, the shape of the square and its dimensions do not change; only its position in the coordinate plane changes.
Since area is determined solely by the lengths of the sides, the area of the translated square remains the same as that of the original square.
Thus, the area of the translated square is:
\[ \boxed{25} \text{ square units} \]