Your controller is covered under warranty, and I would push DJI to repair it. It might not be a Refresh case. File an online warranty claim. You have nothing to lose.
You can try to push it back on, but whether or not it stays depends on whether there is enough of the white mast inside the controller for the button to stay.
The 5d button is a commonly damaged item. Usually when they break off after warranty, I have to replace the whole internal board because they crack off at the bottom of the mast.
If you do decide to try to repair it yourself, I would not use glue. The 5d button is made to move around, and also detaches when the controller needs maintenance. If you use glue, some random glue might get into the pot, and it will never move again. Also, if you permanently affix it, you will have to break it off to remove the cover if the controller ever has a more serious problem.
If all else fails, and you want a controller with a 5d button, I can take yours as a trade-in and send you a used one for not too much money.