The problems are: Roku devices do not show up as a screen mirroring or Airplay choice from your Apple device after updating to Roku 10.5, or the Airplay app on the Roku device briefly tries to launch but then quits.
As far as I'm concerned, the fix is this, (because I have three Roku devices, all of which stopped working with Roku 10.5, but after following the procedure below they all work again):
On your Roku device home screen, go to Settings>System>Power>System Restart>Restart. After it finishes, (the TV will turn TV off, then on again and take 30 seconds or so to get back to the home screen) proceed as follows.
From the home screen on the Roku device go to Settings>Apple Airplay and HomeKit and select. It will reload the Airplay app (it took about 20 seconds on my Roku TV). Now turn on Apple Airplay (it is defaulted off with the reset). Now, when you go back to your apple device, the Roku device should show up as a screen mirroring or Airplay choice.
