5. $f(x)=\frac{x^{3}+7 x}{2-2 x^{2}},|x| \neq 1$ Detailed: Substitute $x$ with $\frac{x-3}{x+1}$ into the original equation, we get $f\left(\frac{3+x}{1-x}\right)+f(x)=\frac{x-3}{x+1}$, then substitute $x$ with $\frac{x+3}{1-x}$ into the original equation, we have $f(x)+f\left(\frac{x-3}{x+1}\right)=\frac{x+3}{1-x}$, adding the two equations yields.
5. Let the function $f(x)$ satisfy $f\left(\frac{x-2}{x+1}\right)+f\left(\frac{3+x}{1-x}\right)=x$ for all real numbers $x$ such that $|x| \neq 1$, then $f(x)=$ $\qquad$