5. Variant 1.

Two square napkins with sizes $1 \times 1$ and $2 \times 2$ were placed on a table such that a corner of the larger napkin fell into the center of the smaller one. What is the maximum area of the table that the napkins can cover?
Answer: 4.75

Solution: The larger napkin covers a quarter of the smaller one. This can be understood by extending the sides of the larger square. Therefore, the area of intersection is 0.25, and the area of the union of the napkins is $1+4-0.25=4.75$