According to Werner's theory of coordination compounds, the ions present outside the coordination sphere (in the ionization sphere) are ionisable. When the complex reacts with silver nitrate ($AgNO_3$), it gives a precipitate of AgCl corresponding to the number of chloride ions present outside the coordination sphere. Since the complex gives two moles of AgCl precipitate per mole of the compound, it must have two ionisable chloride ions outside the square bracket. Among the given options, only $[Co(NH_3)_5NO_3]Cl_2$ satisfies this condition, as it yields two $Cl^-$ ions in aqueous solution.