In the given circuit if the power rating of Zener diode is $$10$$ mW, the value of series resistance $$R_s$$ to regulate the input unregulated supply is: 

$$V_s = 8\text{ V},\quad V_Z = 5\text{ V},\quad R_L = 1\text{ k}\Omega,\quad P_Z = 10\text{ mW}$$

Load current: $$I_L = \frac{V_Z}{R_L} = \frac{5}{10^3} = 5\text{ mA}$$

Maximum Zener current: $$I_Z = \frac{P_Z}{V_Z} = \frac{10\text{ mW}}{5\text{ V}} = 2\text{ mA}$$

Total series current: $$I_s = I_Z + I_L = 2 + 5 = 7\text{ mA}$$

Series resistance: $$R_s = \frac{V_s - V_Z}{I_s} = \frac{8 - 5}{7\text{ mA}} = \frac{3}{7}\text{ k}\Omega$$