4. In the Cartesian coordinate system, if the equation $m\left(x^{2}+y^{2}+2 y+1\right)=(x-2 y+3)^{2}$ represents an ellipse, then the range of values for $m$ is
A. $(0,1)$
B. $(1,+\infty)$
C. $(0,5)$
D. $(5,+\infty)$
Solve:
$$
m\left(x^{2}+y^{2}+2 y+1\right)=(x-2 y+3)^{2} \Rightarrow \frac{\sqrt{x^{2}+(y+1)^{2}}}{\frac{|x-2 y+3|}{\sqrt{5}}}=\sqrt{\frac{5}{m}} \text {. }
$$

The above equation indicates that the ratio of the distance from point $(x, y)$ to point $(0,-1)$ and the distance to the line $x-2 y+3=0$ is equal to the constant $\sqrt{\frac{5}{m}}$, corresponding to an ellipse $\Rightarrow e=\sqrt{\frac{5}{m}} \in(0,1) \Rightarrow m \in(5,+\infty)$. Therefore, the answer is $D$.