You're landing at T3 and departing T5. You'll need to clear security (if going airside) 35 mins prior to departure from T5 to be accepted for travel.

AA has an Arrivals Lounge in T3 which is perfectly acceptable:

http://www.ausbt.com.au/american-qan...row-terminal-3

Best to get to T5 so you don't miss you're flight, though, so it's the Elemis Spa showers at the South or North Lounges for you:



Either are acceptable, but there are more at South lounges. I've never had to wait more than 5 mins.