[Fire TV Themes and Apps] LakituLives:
I can confirm the same. Using Fire TV Stick on Fire OS 5 Dev Preview. I can launch the launcher manually through the stock settings menu but the access to the home button and launching apps at boot is not working as it should.

As for errors:

1. FireStarter: Exception: Clearing logcat failed.

2. FireStarter: Something went wrong , restarting HomeButtonObserver now...

Error log:

I/art ( 3821): WaitForGcToComplete blocked for 9.573ms for cause HeapTrim
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): Starting HomeButtonObserver.
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): CONNECTHREAD: try connect to localhost
W/khrn_client( 3821): init_window num_buffers 3 min undequeued buffers 1
W/BufferQueueProducer( 174): BufferQueueProducer : Detecting broadcom driver request, using jellybean logic
W/khrn_client( 3821): init_window window 0x467be010, 880x125 hintTransform 0x0 do_pre 0
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): CONNECTHREAD: adb received: already connected to localhost:5555
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): Adb is connected, check devices..
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): GETADBDEVICETHREAD: try get adb device
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): GETADBDEVICETHREAD: adb received: List of devices attached
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): emulator-5554	offline
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): localhost:5555	offline
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821):
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): GETADBDEVICETHREAD: adb device found: localhost:5555
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): Adb device found, empty logcat..
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): EMPTYLOGCATTHREAD: try clear logcat
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): EMPTYLOGCATTHREAD: Try to kill running process
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): GetUnixPID: process name: java.lang.ProcessManager$ProcessImpl
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): KillUnixProcess: pid: 4870
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): EMPTYLOGCATTHREAD: adb received: - waiting for device -
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): EMPTYLOGCATTHREAD: device name must be wrong..
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): EMPTYLOGCATTHREAD: Killed running process successful
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): Error in BackgroundObserver:
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): java.lang.Exception: Clearing logcat failed.
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821):	at de.belu.firestarter.observer.BackgroundHomeButtonObserverThread.run(BackgroundHomeButtonObserverThread.java:343)
D/de.belu.firestarter.observer.BackgroundHomeButtonObserverThread( 3821): Restart observer in a few seconds..
W/khrn_client( 3821): init_window num_buffers 3 min undequeued buffers 1
W/BufferQueueProducer( 174): BufferQueueProducer : Detecting broadcom driver request, using jellybean logic
W/khrn_client( 3821): init_window window 0x467be010, 657x88 hintTransform 0x0 do_pre 0

I see in the OP you mention a logcat event when the homebutton is used. It looks like logcat is still reporting as it did in Fire OS 3.

Logcat shows the following while in Fire OS 5:

W/TelecomManager( 530): Telecom Service not found.
I/ActivityManager( 530): START u0 {act=android.intent.action.MAIN cat=[android.intent.category.HOME] flg=0x10200000 cmp=com.amazon.tv.launcher/.ui.HomeActivity} from uid 1000 on display 0
I/ActivityManager( 530): START u0 {act=android.intent.action.VIEW cat=[com.amazon.device.intent.category.LAUNCHER_MENU] flg=0x14000000 cmp=com.amazon.tv.launcher/.ui.HomeActivity (has extras)} from uid 32059 on display 0

Perhaps this is due to selinux being restrictive.. but hopefully just an issue of android 4.2.2 vs 5.1 changes. I am available and capable for testing on Fire OS 5 if needed.