Step 1: Ionisation isomerism occurs when two complexes differ in the counter ions present inside and outside the coordination sphere. Step 2: In \([Co(NH_3)_5Br]SO_4\), the bromide ion is coordinated to cobalt, and sulfate is the counter ion. In \([Co(NH_3)_5SO_4]Br\), the sulfate ion is coordinated to cobalt, and bromide is the counter ion. Step 3: These two complexes produce different ions in solution: - The first gives \( Br^- \) inside the complex and \( SO_4^{2-} \) as free ion. - The second gives \( SO_4^{2-} \) inside the complex and \( Br^- \) as free ion. Step 4: Therefore, they are ionisation isomers.