Step 1: Compare what each complex sets free in water. A quick test tells them apart: one solution gives a precipitate with BaCl2 (free sulphate), the other gives a precipitate with AgNO3 (free bromide).
Step 2: [CoBr(NH3)5]SO4 keeps Br- firmly bound to Co and lets SO42- ionise, so it responds to BaCl2. [CoSO4(NH3)5]Br does the opposite, releasing Br- and responding to AgNO3.
Step 3: Because the only change is which anion sits inside the metal sphere and which sits outside as the ionising counter ion, the pair are ionisation isomers.
Result: The answer is ionisation isomerism, alternative (iii).