\[\sin{35{^\circ}} \cdot \cos{5{^\circ}} =\]
\[= \frac{1}{2} \cdot \left( \sin{40{^\circ}} + \sin{30{^\circ}} \right) =\]
\[= \frac{1}{2} \cdot \left( \sin{40{^\circ} + \frac{1}{2}} \right) =\]
\[= \frac{1}{2}\sin{40{^\circ}} + \frac{1}{4}\]