If the two numbers are a and b, then the geometric mean between them is given by $\rm GM = \sqrt{ab}$.

Given,

$\rm a = -4$ and $\rm b = -25$

By substituting the values into the formula, we get,

$\rm or, GM = - \sqrt{ab}$

$\rm or, GM = - \sqrt{ 4 \cdot 25 }$

$\rm or, GM = - \sqrt{100}$

$\rm or, GM = - \sqrt{ 10^{2} }$

$\rm \therefore GM = - 10$

Hence, the required geometric mean between the numbers $\rm -4$ and $\rm -25$ is $\rm -10$.