[b]Remind the following steps to solve a Geometry question.
1. Write down all conditions given in a question.
2. If we don't have any clue at step 1, we should try to find out any proper adjoint lines.[\b]
In this question, the heights are their adjoint lines.

The triangle with the base $5$ is the height $4$ and the triangle with the base $4$ has the height $\sqrt{21}$ from Pythagorean Theorem, since we have $5^2 = 2^2 + \sqrt{21}^2$ and $5^2 = 3^3 + 4^2$.
Then we have $x = \sqrt{21} - 4$.
Since we have $4 = \sqrt{16} < \sqrt{21} < \sqrt{25} = 5$, we have $0 < x = \sqrt{4} < 5 - 4 = 1$ or $x < 1$.

Therefore, A is the right answer.