5. Given the ellipse $E: \frac{x^{2}}{m}+\frac{y^{2}}{4}=1$, for any real number $k$, the following line 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) $k x+y-2=0$
5. D.

When $k=1$, option (A) is correct;
When $k=0$, option (B) is correct;
When $k=-1$, option (C) is correct;