Try invalidating your project and gradle cache as Oleg and I suggested.
To clear Gradle cache - delete everything related to Backendless at
Project cache can be invalidated in your IDE - File > Invalidate Caches/ Restart (then click Invalidate and restart)
Android Studio makes a lot of files as caches and deletes them on request. This may be causing issues including yours.
According to the stacktrace you posted (lines 143 and 94 of BackendlessBroadcastReceiver.java) your project still references
3.x library, you can see it here: https://github.com/Backendless/Android-SDK/blob/3.X/src/com/backendless/push/BackendlessBroadcastReceiver.java
BackendlessBroadcastReceiver class is completely different in v4-5 of Backendless, it contains less then 80 lines of code: https://github.com/Backendless/Android-SDK/blob/master/src/com/backendless/push/BackendlessBroadcastReceiver.java
Please try invalidating caches, when done -
build your project, repeat your message publishing/receiving scenario and let us know about results.