If $y=f\left(x\right)=\frac{5x+3}{4x-5}$ then $f\left(y\right)=$

Given $y=f\left(x\right)=\frac{5x+3}{4x-5}$

Consider 

$\begin{array}{rcl}f\left(y\right)& =& f\left(\frac{5x+3}{4x-5}\right)\\ & =& \frac{5\left(\frac{5x+3}{4x-5}\right)+3}{4\left(\frac{5x+3}{4x-5}\right)-5}\\ & =& \frac{25x+15+12x-15}{20x+12-20x+25}\\ & =& \frac{27x}{27}\\ & =& x\end{array}$

Therefore, $f\left(y\right)=\boxed{x}$