Since $(-3) \begin{pmatrix} 4 \\ 7 \end{pmatrix} = \begin{pmatrix} -12 \\ -21 \end{pmatrix},$ the scale factor of the dilation is $-3.$  So the vector $\begin{pmatrix} -2 \\ 5 \end{pmatrix}$ is taken to $\begin{pmatrix} 6 \\ -15 \end{pmatrix}.$
A dilation centered at the origin takes $\begin{pmatrix} 4 \\ 7 \end{pmatrix}$ to $\begin{pmatrix} -12 \\ -21 \end{pmatrix}.$  Which vector does the dilation take $\begin{pmatrix} -2 \\ 5 \end{pmatrix}$ to?