$$V_{ring} = 5.3 \ mL - 5.0 \ mL = 0.3 \ mL = 0.3 \ cm^3$$

Since the density of platinum is 21 g/cm3, the mass of the ring is:

$$m_{ring} = \rho V_{ring} = (21 \ g/cm^3)(0.3 \ cm^3) = 6.3 \ g$$

Therefore, the mass of the platinum ring is 6.3 g.