I cannot delete the photos that were synced from my pc to my iphone 5s. I followed instructions posted, but it does not work

You delete by syncing again with iTunes using the instructions below from Sync photos from your computer to your iOS device using iTunes - Apple Support

If the method in the first 4 steps doesn't work, try the method in the link at the very bottom:

Delete synced photos

1. In iTunes, locate and click on your device.
2. Click Photos.
3. Choose "Selected albums" and deselect the albums or collections you want to delete.
   To delete all synced photos, deselect "Sync Photos from" and, when asked, click "Remove photos."
4. Click Apply.

Learn how to delete photos and video synced from iTunes when you can't access the originals.