How to delete an gpx route downloaded on a Fenix 5 ? Directly on the watch ? With Connect ?

Directly on the watch: 

Press Start button >
   select Navigate >
   long press Menu button >
   select Navigation > press start button >
   select Courses > press start button >
   select Course to delete > press start button >
   select Delete > press start button >
   select Yes > press start button

With GC from the Menu:
   Select Training > Courses > place the cursor at the course to delete > klick on the trash on the right side of the course

With GCM it's mainly the same as with GC:
   Select Training > Courses > select course to delete > tap at the at the 3 points at the upper right corner and select delete

I hope I havn't forgotten something ;-D

With GC and GCM the watch must be synced subsequently.

It's also possible to connect the watch with a PC via USB and switch to the directory "Garmin/Courses..." and delete the course. But be sure it's the right course that you want to delete.