how do i delete photos if the trash icon isn't available

If you have photos on the phone that were synced to it from a computer, the trash icon won't be available for those photos. Delete them by syncing again without those photos selected to sync.

See: Sync your photos manually using the Finder - Apple Support or Sync photos in iTunes on PC with devices - Apple Support

I have repeatedly tried turning off syncing photos to my iphone, and selecting the option that asks if I want previously synced items deleted, but it does not delete them. and I still get a greyed out trash icon when I try to select and delete on my iphone. or else it allows me to select and push delete but then I get a message that says only that it will delete the shared photos and it does not delete the rest of them.

Help!!! my phone is drowning in photos and it seems impossible to take them off, which is absurd! I am wasting huge amounts of time trying to figure this out!