Answer $(2,3)$.
Analysis Since
$$
f(-x)=\frac{1-4^{-x}}{2^{-x}}+x=\frac{4^{x}-1}{2^{x}}+x=-f(x)
$$

Therefore, $f(x)$ is an odd function and a decreasing function on $\mathbf{R}$. From $f\left(1-x^{2}\right)+f(5 x-7)x^{2}-1$, we get $x^{2}-5 x+6<0$, solving this yields: $2<x<3$.
4. Let the function $f(x)=\frac{1-4^{x}}{2^{x}}-x$, then the solution set of the inequality $f\left(1-x^{2}\right)+f(5 x-7)<0$ is