we know that
−5pi/4----------> -1.25 pi---------> belong to the third quadrant
1.25 pi-------> (pi+pi/4)
cot (−5pi/4)=-cot (pi/4)
pi/4=45°
cot (45°)=1
then
cot (pi/4)=1
cot (−5pi/4)=-1-----------> is negative because belong to the third quadrant
the answer is
cot (−5pi/4)=-1