Half-half-half!

$1\space curie\space (Ci) = 3.7\times 10^{10}$ atoms decaying per second.

In terms of $mol$ and half life $t_{\frac{1}{2}}$ :

$1\space Ci = \cfrac{3.7\times 10^{10}}{(\ln{2})N_A} \times t_{\frac{1}{2}} mol$

where $N_A = 6.0221\times 10^{23}/mol$ is the Avogadro constant.

For $^{210}Po$ , $1 mol=210 g$ , $t_{\frac{1}{2}} = 138\space days$ and one $\alpha$ particle for one atom decayed,

$\Rightarrow 5\space mCi = \cfrac{3.7\times 10^{10}\times 138\times 24\times 60\times 60\times 0.005}{\ln{2}\times 6.0221\times 10^{23}}=\boxed{1.11\times 10^{-6}g}$