3. Answer: 10

Analysis: As shown in the figure, connect $\mathrm{AB}$ and $\mathrm{CD}$ intersecting at 0. It is easy to obtain the area of triangle $\mathrm{ACH}$ using the Pythagorean theorem and the formula for the area of a semicircle, which means the area of triangle $\mathrm{AOC}$ is equal to the sum of the areas of the two "crescents" on $\mathrm{AH}$ and $\mathrm{HC}$. Therefore, the total area of these 8 "crescents" is equal to the area of square ACBD.

Since the total area of these 8 "crescents" is 5 square centimeters, and the area of square EFGH is twice the area of square ACBD, the area of square EFGH is 10 square centimeters.
As shown in the figure, the vertices of the shaded square are the midpoints of the sides of the larger square $\mathrm{EFGH}$. Semi-circles are drawn outward with half the sides of the larger square as diameters, and then semi-circles are drawn outward with the sides of the shaded square as diameters, forming 8 "crescent shapes". The total area of these 8 "crescent shapes" is 5 square centimeters. What is the area of the larger square EFGH in square centimeters?