Answer
$Q < Ksp$ so all salt is dissolved.
Work Step by Step
$[SrSO_4](initial)=5.0\ mg\div10^3\ mg/g\div 183.68\ g/mol\div 1.0\ L=2.72\times10^{-5}\ M$
$Q = [Sr^{2+}][SO_4^{2-}]=(2.72\times10^{-5})^2=7.41\times10^{-10}$
$Ksp = 3.44\times10^{-7}$
$Q < Ksp$ so all salt is dissolved.