Coordinate statement

For (1), 405 is the angle of the first quadrant, but it is not an acute angle, and the proposition (1) is wrong;

For (2), the terminal edges of 45 and 405 are the same, but not equal, and the proposition (2) is wrong;

For (3), the equilateral ends must be the same and correct, and the proposition (3) is correct;

For (4), the angle of 0 is less than 90, but the angle of 0 is not acute, so the proposition (4) is wrong;

For (5), the range of obtuse angle is (90, 180), and the terminal edge of obtuse angle is in the second quadrant, so the proposition (5) is correct;

For (6), the quadrant angle of the terminal edge on the straight line y=3x is expressed as k 180 +60 60, k∈Z, and the proposition (6) is wrong.

The correct statement is (3)(5).

So the answer is: (3)(5).