5. i will arrange $1 \times 1$ square tiles into a strip with a diagonal length of 100. Find the approximate minimum value of the total length of the cuts, not exceeding 2.
For $a>$. $a^{2}+b^{2}=100^{2}, ab=1$,
$$
\therefore c+b=\sqrt{100^{2}+2}>100 .
$$

The perimeter of the rectangle $2(a+b)$ is due to the original square's perimeter.

Given its two uses, $2 L+4 \geqslant 2(a+b)$, $L \geqslant a+b-2>98$.
On the other hand,

Any two parallelograms with the same base and height can be:
tightly arranged in the manner shown in the right figure,
taking $ABCD$ as a parallelogram with length $a$ and height $b$, then one length is $a+b$, so $L \leqslant a+b<100.01$.
Therefore, $L \approx 99$, with an error of no more than 1.01.