In order to perform the given transformation, we just have to replace the x and y-coordinates into the transformation rule, like this:
A(5, 7), by replacing 5 for x and 7 for y into (x - 5, -y + 2), we get:
(5 - 5, -7 + 2) = (0, -5)
A(5, 7) -> A'(0, -5)
Then, the coordinates of the new point A' are (0, -5)