Starship flight 6 launch seems to have two guesses as to launch date. Supposedly the internal goal is for Nov 11. The other date being discussed is Nov 23 which is SpaceX's president Gwen Shotwells birthday. Some folks are reporting that Flight 6 is also waiting FAA approval. Other have said Fight 6 was approved at the same time as Flight 5. As mentioned, the booster just had its static fire test, have not see a report on if it was deemed successful or not. Starship for flight 6 has already had its static fire test done. The question is, will SpaceX update all the heat shield tiles on the ship for flight 6 to the ones they used on flight 5, or will they just use the ones that are already installed? They are replacing some critical tiles and some testing tiles. This may be a key for a Nov 11 or Nov 23 launch.
Also discussed, but still unknown, is for Starship going for a 'catch' on flight 7.
Saw today that SpaceX only has approval for 6 flights per year from TX. SpaceX is looking to address this and to finish launch tower in FL.