Let $e_1$ and $e_2$ be the eccentricities of the ellipse $\frac{x^2}{25}+\frac{y^2}{b^2}=1 \left(b<5\right)$ and the hyperbola $\frac{x^2}{16}-\frac{y^2}{b^2}=1$ respectively satisfying ${\mathrm{e}}_1{\mathrm{e}}_2=1$. If $\alpha$ and $\beta$ are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair $\left(\alpha , \beta \right)$ is equal to: