How can I delete old photos from my iPhone?

Sounds like you tried deleting but they have no trash can symbol?

If so they were probably sync'd from a computer. You can re-sync with no selection on the sync panel.

If that doesn't work you may have to backup and restore.

Failing that, and it would be last resort, you will have to selectiveky move all your data elsewhere, Erase all content and settings, then build up from scratch,

You're welcome, good luck.