The Yamaimo family is moving to a new house, so they’ve packed their belongings into boxes, which weigh $100\text{ kg}$ in total. Mr. Yamaimo realizes that $99\%$ of the weight of the boxes is due to books. Later, the family unpacks some of the books (and nothing else). Mr. Yamaimo notices that now only $95\%$ of the weight of the boxes is due to books. How much do the boxes weigh now in kilograms?
1. Before unpacking, the total weight of the boxes is \(100 \text{ kg}\).
2. \(99\%\) of the weight is due to books, so the weight of the books is:
   \[
   99\% \times 100 \text{ kg} = 99 \text{ kg}
   \]
3. The weight of non-books is:
   \[
   100 \text{ kg} - 99 \text{ kg} = 1 \text{ kg}
   \]
4. Let \(x \text{ kg}\) be the weight of books remaining in the boxes after unpacking.
5. After unpacking, the weight of non-books remains \(1 \text{ kg}\), and this is now \(5\%\) of the total weight of the boxes.
6. Therefore, we have:
   \[
   1 \text{ kg} = 5\% \times (x + 1 \text{ kg})
   \]
7. Converting \(5\%\) to a decimal, we get:
   \[
   1 \text{ kg} = 0.05 \times (x + 1 \text{ kg})
   \]
8. Solving for \(x\):
   \[
   1 \text{ kg} = 0.05x + 0.05 \text{ kg}
   \]
   \[
   1 \text{ kg} - 0.05 \text{ kg} = 0.05x
   \]
   \[
   0.95 \text{ kg} = 0.05x
   \]
   \[
   x = \frac{0.95 \text{ kg}}{0.05}
   \]
   \[
   x = 19 \text{ kg}
   \]
9. The total weight of the boxes after unpacking is:
   \[
   x + 1 \text{ kg} = 19 \text{ kg} + 1 \text{ kg} = 20 \text{ kg}
   \]

The final answer is \(\boxed{20 \text{ kg}}\).