Find $f(5)$ where $f$ satisfies $f(x)+f(1/(1-x))=x $

$$f\left(5\right)+f\left(-\frac14\right)=5$$

If we know $f\left(-\frac14\right)$, we can solve the problem.

$$f\left(-\frac14\right)+f\left(\frac45\right)=-\frac14$$

If we know $f\left(\frac45 \right)$, we can solve the problem.

$$f\left(\frac45\right)+f\left(5\right)=\frac45$$

Why don't we just solve the linear system? Are you able to solve it?

You can use the fact that$$\left( \frac{1}{1-x} \right)^{-1}=1-\frac{1}{x},$$where the exponent $-1$ stands for the reverse. If you substitute $1/(1-x)$ and $1-1/x$ in the functional equation and solve three simultaneous equations, you can find general form of $f(x)$.