In the given circuit if the power rating of Zener diode is 10mW ,...

Potential drop across ${R}_{s}$, 

${V}_{1} = 8 - 5 = 3V$

Current through the load resistor

$I = \dfrac{5}{1 \times {10}^{3}} = 5mA$

Maximum current through Zener diode

${I}_{Z, max} = \dfrac{10}{5} = 2mA$

And minimum current through Zener diode

${I}_{Z, min} = 0$

$∴ {I}_{S, max} = 5 + 2 = 7mA$

And ${R}_{S, min} = \dfrac{{V}_{1}}{{I}_{S, max}} = \dfrac{3}{7}kΩ$

Similarly,

${I}_{S, min} = 5mA$

And ${R}_{S, max} = \dfrac{{V}_{1}}{{I}_{S, min}} = \dfrac{3}{5}kΩ$

$∴ \dfrac{3}{7}kΩ < {R}_{s} < \dfrac{3}{5}kΩ$