If cos A = -5/13, what is cos (A - pi/4) ? It wants the answer in exact form.

Hello!
There is a formula cos(a-b)=cos(a)cos(b)+sin(a)sin(b).
In our case, a=A and b=pi/4, and we know cos(pi/4)=sin(pi/4)=sqrt(2)/2. So 
cos(A-pi/4) = cos(A)cos(pi/4)+sin(A)sin(pi/4)=sqrt(2)/2(cos(A)+sin(A)).
 
cos(A) is given, what about sin(A)? Of course cos^2(A)+sin^2(A)=1, so
sin(A) = +-sqrt(1-cos^2(A))=+-sqrt(1-25/169) = +-sqrt(144/169) = +-12/13.
 
To select "+" or "-" we have to know something additional about A. If it resides in the II quadrant, then "+", if in the III quadrant, then "-" (it cannot reside in the I or IV quadrants because its cosine is negative).
Without any additional information, we can only state that the answer is either  sqrt(2)/2*7/13  or  -sqrt(2)/2*7/13.