Firstly, observe that $u_n \geq u_{n+5}-5 \geq u_{n+10}-10 \geq u_{n+8}-8 \geq u_{n+6}-6\geq u_{n+4}-4 \geq u_{n+2}-2 \geq u_n$ So equality must hold everywhere. From the equality $u_n=u_{n+2}-2=u_{n+5}-5$ we see that for every $n,a,b \in \mathbb{N}$ , $u_{n}+5a+2b=u_{n+5a+2b}$ Thus $u_{2023}=u_0+2023=2123$ ($n=0,a=1,b=1009$)