1. **State the problem:** We have two similar hexagons with corresponding sides measuring 2 cm and 5 cm. 2. **Understand similarity:** Similar polygons have corresponding sides in proportion. The ratio of any pair of corresponding sides is the same. 3. **Formula:** If the sides of the smaller hexagon are $s_1$ and the larger hexagon are $s_2$, then the scale factor $k$ is given by: $$k = \frac{s_2}{s_1}$$ 4. **Calculate the scale factor:** $$k = \frac{5}{2} = 2.5$$ 5. **Interpretation:** This means every side of the larger hexagon is 2.5 times the length of the corresponding side of the smaller hexagon. 6. **Additional properties:** Since the hexagons are similar, their areas relate by the square of the scale factor: $$\text{Area ratio} = k^2 = (2.5)^2 = 6.25$$ This means the larger hexagon's area is 6.25 times the smaller hexagon's area. **Final answer:** The scale factor between the hexagons is $2.5$, and the area ratio is $6.25$.