8. Let $z_{1} 、 z_{2}$ be complex numbers, and satisfy:
$$
\left|z_{1}\right|=5, \frac{z_{1}}{z_{2}}=2+\mathrm{i} \text {. }
$$

Then $\left|z_{1}-z_{2}\right|=$
8. $\sqrt{10}$.

Given $\left|z_{1}\right|=5$, we can set $z_{1}=5(\cos \alpha+\mathrm{i} \sin \alpha)$. Substituting into $\frac{z_{1}}{z_{2}}=2+\mathrm{i}$, we get $z_{2}=(2-\mathrm{i})(\cos \alpha+\mathrm{i} \sin \alpha)$.
Therefore, $\left|z_{1}-z_{2}\right|=|(3+\mathrm{i})(\cos \alpha+\mathrm{i} \sin \alpha)|$ $=\sqrt{10}$