sin A = 5/13

A is obtuse (a second quadrant angle between 90° and 180°)

If you draw a second quadrant triangle, you will get a triangle whose sides are 5 (opposite length), -12 (adjacent length) and 13 (hypotenuse).

You know why it's -12 correct?

So, from here, we can see that

cos A = -12/13 and
tan A = -5/12,

indicative of the negative trigonometric ratios for cosine and tangent in the second quadrant.

Let's look at the questions now.

sec A
= 1 / cos A
= 1 / (-12/13)
= -13/12

Up next will be your negative angle identity. Let me know if you need to elaborate further on this.

cos (-A)
= cos A (no negative sign in front of cos A!)
= -12/13

Up next will be your complementary angle rule.

tan (90° - A)
= 1 / tan A
= 1 / (-5/12)
= -12/5