5. Given the ellipse $E: \frac{x^{2}}{m}+\frac{y^{2}}{4}=1$, for any real number $k$, among the following lines, the one whose chord length intercepted by the ellipse $E$ cannot be equal to the chord length intercepted by the line $l: y=k x+1$ on the ellipse $E$ is
A. $k x+y+k=0$
B. $k x-y-1=0$
C. $k x+y-k=0$
D. $k x+y-2=0$
Solve
\[
\left\{
\begin{array}{l}
4 x^{2}+m y^{2}=4 m, \\
y=k x+1
\end{array}
\Rightarrow\left(m k^{2}+4\right) x^{2}+2 m k x-3 m=0
\right.
\]
\[
\Rightarrow \Delta_{1}=4 m^{2} k^{2}+12 m\left(m k^{2}+4\right)=16 m^{2} k^{2}+48 m.
\]
\[
\left\{
\begin{array}{l}
4 x^{2}+m y^{2}=4 m, \\
-y=k x-2
\end{array}
\Rightarrow\left(m k^{2}+4\right) x^{2}-4 m k x=0 \Rightarrow \Delta_{2}=16 m^{2} k^{2}
\right.
\]
Clearly, \( m>0 \Rightarrow \Delta_{1} \neq \Delta_{2} \), so the answer is \( D \).