Samsung created a quite easy way to sign up for the new Android 13-based One UI 5.0 Beta program

Just download the Samsung Members app from the Play Store or Galaxy Store

you should have a notice regarding One UI 5 Beta registration

tap on it and an entry form will appear so you can fill in your details.

Now, the company will show you the terms and conditions of the One UI Beta program

read them carefully then hit the ENROLL button to conclude the Beta joining procedure.

Now go to Settings > Software Updates > Download and Install and proceed with software installation