8. $(3-\sqrt{2}, 3+\sqrt{2})$

Analysis: The original inequality can be transformed into: $\left|\sqrt{(x-1)^{2}+3}-\sqrt{(x-5)^{2}+3}\right|<2$
That is: the absolute value of the difference in distances from a point $(x, \sqrt{3})$ on the plane to $(1,0),(5,0)$ is less than 2.
Since the hyperbola $x^{2}-\frac{y^{2}}{3}=1$ intersects with $y=\sqrt{3}$ at points $(-\sqrt{2}, 0),(\sqrt{2}, 0)$, the solution to the original inequality is $(3-\sqrt{2}, 3+\sqrt{2})$.