Why would QF move to T5? BA doesn't have enough space for their own flights there as T5 currently exists. The only other airline in T5 is IB, which is the same company as BA.
QF moved from T4 to T3 during the airline moves when T5 opened to be with the rest oneworld (that were oneworld members at the time).
At some point, T2 is going to be expanded into the space occupied by T3 and T5 is going to get another concourse with the existing concourses extended to fit a few more gates, with the plan to have T2 and T5 in a "toast rack" layout between the existing runways, T4 to the south and maybe a new T6 to the north with the expected 3rd runway. Given that this was already meant to have happened, and hasn't, it is anyone's guess as to when it actually will. Until such time as there are more gates at T5, there is no possibility that QF, or any other oneworld non BA/IB flight, moving into T5.