jmc

Since $f$ is a linear function, it has the form $f(x)=mx+b$. Because $f(1)\le f(2)$, we have $m\ge 0$. Similarly, $f(3)\ge f(4)$ implies $m\le 0$. Hence, $m=0$, and $f$ is a constant function. Thus, $f(0)=f(5)=5$, which means $\boxed{\text{D}}$ is true.