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From (x - y = 3), we can express (x) as (x = y + 3). Substituting this into (x^2 + y^2 = 25), we get ((y + 3)^2 + y^2 = 25). Expanding and simplifying, we get (2y^2 + 6y + 9 = 25). Subtracting 9 from both sides, we get (2y^2 + 6y - 16 = 0). Factoring, we get ((2y - 4)(y + 4) = 0). Therefore, (y = 2) or (y = -4). If (y = 2), then (x = y + 3 = 2 + 3 = 5). Therefore, (x + y = 5 + 2 = 7). If (y = -4), then (x = y + 3 = -4 + 3 = -1). Therefore, (x + y = -1 + (-4) = -5). Since (x + y) cannot be negative, the correct answer is (7).