It used to be easy. I have no idea when I lost the ability to delete text messages, because I haven't needed to do it for a long time. With iOS version 10.3.3 on my iPhone 5, there doesn't appear to be any way of deleting a text message, unless I delete the sender, in which case it will delete all of his messages. How do I delete individual messages?

The problem I'm having is that an idiot friend of mine has suddenly started spamming everyone in his contact list with stupid photos that he thinks are funny. I don't want to hurt his feelings by telling him to stop, but I'm getting close to that point.

See my reply here.

Awesome. Thank you.
I'd tried just about everything except "tap and hold"

Summarizing the info at dkmarsh's link:
- Open the messages conversation, then tap and hold on any text or image within the message dialog
- Choose “More” from the pop-up menu, then tap on the messages to delete so that a checkbox appears next to them
- Tap the Trash icon in the corner, then confirm the message deletion by choosing “Delete Message”

Epilog:
My idiot friend just got his first phone bill after switching to his new phone plan, and discovered that he was being charged $0.75 for every photo that he'd texted. So, karma is back in balance.