Lift and remove the home button assembly.

You can reuse the home button gasket if it's sufficiently tacky. Otherwise, replace the black rubber gasket:

Peel the gasket off of the home button. Then, thread it past the cable to remove it.

Apply a replacement gasket to the home button.

The iPad mini 4's replacement gasket fits on the iPad mini 5, but it is slightly larger. Make sure it doesn't overlap the screen's adhesive so that the screen can be properly adhered to the frame.

To install the home button:

Rotate the home button so that the home button cable sits where it was before disassembly. Make sure the home button cable can be inserted into its ZIF connector.

Center the home button so that it fits into its slot in the screen. Then, press down firmly on the gasket to adhere it to the screen.