These compounds give different ions in aqueous solution. This can be tested by using AgNO₃ solution and BaCl₂

[Co(NH₃)₅Cl]SO_4(aq) + BaCl_2(aq) → BaSO_4(ppt)

[Co(NH₃)₅Cl]SO_4(aq) + AgNO_3(aq) → no reaction

[Co(NH₃)₅(SO₄)]Cl_(aq) + BaCl_2(aq) → no reaction

[Co(NH₃)₅(SO₄)]Cl_(aq) + AgNO_3(aq) → AgCl_(ppt)

Hence they give different precipitates with different solutions. Thus they are ionisation isomers.