Question about moment! please answer and help thanks?

I am afraid the "model answer" is wrong.

You are right that the equation should be,
(N1).(0.6+0.9)/cos(5) = 0.9mg

In the model answer, only the resolved (vertical) component N1.cos(5) is considered. The other resolved (horizontal) component N1.sin(5) has been neglected.

If the component N1.sin(5) is also taken into consideration, then the clockwise moment becomes N1.cos(5).(0.6+0.9) + N1.sin(5).y
where y is the vertical distance between B and the horizontal line at the level of A. From geometry, tan(5) = y/(0.6+0.9), or y = 1.5.tan(5)

Hence, the clockwise moment becomes,
N1.cos(5).(1.5) + N1.sin(5).(1.5.tan(5))
= 1.5(N1).cos(5) + 1.5(N1)sin(5).sin(5)/cos(5)
= 1.5(N1)[(cos^2(5) + sin^2(5)]/cos(5)
= 1.5(N1)/cos(5) [because cos^2(5) + sin^2(5) = 1 ]

This is just the clockwise moment that you suggested.

In fact, in this problem, it is not necessary to resolve the force N1 into vertical and horizontal components. This makes the calculation even more clumsy. Since N1 is already perpendicular to AB, the moment is just simply (N1).(AB)