5. (5 points) The side length of square $A$ is 10. If the side lengths of squares $B$ and $C$ are both natural numbers, and the sum of the areas of $B$ and $C$ equals the area of $A$, then the sum of the side lengths of $B$ and $C$ is $\qquad$
【Analysis】This problem illustrates that the areas of two squares $B$ and $C$ are equal to the area of $A$, which conforms to the Pythagorean theorem. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, the solution can be derived.

【Solution】Solution: According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, one of the squares has a side length of 10. Based on the Pythagorean triplet $6,8,10$:
$6^{2}+8^{2}=10^{2}$ satisfies the condition.
$$
6+8=14,
$$

Therefore, the answer is: 14.