5) \(\cos(55^\circ)\cos(25^\circ)+\sin(55^\circ)\sin(25^\circ)\)

По формуле \(\cos(A-B)=\cos A\cos B+\sin A\sin B\):

\(\cos55^\circ\cos25^\circ+\sin55^\circ\sin25^\circ=\cos(55^\circ-25^\circ)=\cos30^\circ=\frac{\sqrt3}{2}.\)

Ответ: \(\frac{\sqrt3}{2}\).