Having been through T2 security twice in the last 3 weeks I would suggest you should allow 5 to 10 minutes to clear security
For a 9:20 flight I would aim to be in the airport around 7:20 so leaving the hotel around 7
IMO a taxi at 5:30 would be far too early, I would not even by out of bed by then.
I had a 12:30 departure this week, HBO, I left the Hilton doubletree further along the bath road at 10:30, caught the bus and was in the security line around 11, in the lounge by 11:15