Answer
See the answer below.
Work Step by Step
Pure water:
$Ksp=[Ba^{2+}]F^-]=s\dot{}(2s)^2$
$s=\sqrt[3]{1.8\dot{}10^{-17}/4}=1.65\dot{}10^{-6}\ M$
$s^*=1.65\dot{}10^{-6}\ mol/L\dot{}175.32\ g/mol=2.89\dot{}10^{-4}\ mg/mL$
With KF:
$[KF]=5.0\ g/L\div 58.10\ g/mol=0.086\ M$
$Ksp=s\dot{}(2s+0.086)^2$
$s=2.43\dot{}10^{-15}\ M$
$s^*=2.43\dot{}10^{-15}\ mol/L\dot{}175.32\ g/mol=4.26\dot{}10^{-13}\ mg/mL$