5. After sawing off a strip of width $\frac{1}{2}$ meter from a square wooden board, the remaining area is $\frac{65}{18}$ square meters. What is the area of the sawn-off strip in square meters?
5. The area of the wooden strip sawed off is $1 \frac{1}{12}$ square meters.
5. 【Solution】Four rectangular pieces with an area of $\frac{65}{18}$ square meters each are assembled into the square shown below, with a small square left empty in the center. The side length of this small square is $\frac{1}{2}$ meters.

The area of the large square is: $\frac{65}{18} \times 4 + \left(\frac{1}{2}\right)^{2} = \frac{260}{18} + \frac{1}{4} = \frac{529}{36}$ (square meters).

Since $\frac{23}{6} \times \frac{23}{6} = \frac{529}{36}$, the side length of the large square is $\frac{23}{6}$ meters.

The side length of the large square is $\frac{1}{2}$ meter less than twice the side length of the original square, so the side length of the original square is $\left(\frac{23}{6} + \frac{1}{2}\right) \div 2 = \frac{26}{6} \div 2 = \frac{13}{6}$ (meters).

The area of the sawed-off wooden strip is $\frac{13}{6} \times \frac{1}{2} = 1 \frac{1}{12}$ (square meters)