5. (10 points) The figure below shows a fragment of a wall paved with square tiles, each 1 square decimeter in area. Question: What is the area, in square decimeters, of the quadrilateral $ABCD$ with vertices at grid points $A, B, C, D$?
【Analysis】This is a problem involving lattice points in a square grid. According to Pick's theorem for a square lattice, $S=\mathbf{N}-1+L \div 2$, the area can be directly calculated, where $N$ represents the number of interior lattice points, and $L$ represents the number of boundary lattice points.

【Solution】Solution: The number of interior lattice points is 12, and the number of boundary points is 6. According to the formula, the equation is
$$
12-1+6 \div 2=14
$$

Answer: The area of quadrilateral $A B C D$ is 14 square decimeters.