$\text{ If }f\text{ is a function such that }f\left(0\right)=2,f\left(1\right)=3\text{ and }f(x+2)$ $=2f\left(x\right)-f(x+1)\text{ for every real }x\text{ then }f\left(5\right)\text{ is }$ 

$\text{ Put }x=0\Rightarrow f\left(2\right)=2f\left(0\right)-f\left(1\right)=2\times 2-3=1$

$\begin{array}{l}put,x=1\Rightarrow f\left(3\right)=6-1=5\\ put,x=2\Rightarrow f\left(4\right)=2f\left(2\right)-f\left(3\right)=2\times 1-5=-3\\ put,x=3\Rightarrow f\left(5\right)=2f\left(3\right)-f\left(4\right)=2\left(5\right)-(-3)=13\end{array}$