Is there a way of retrieving data that you looked at in private mode. The phone is a iphone 5?

I've gone into settings, safari, advanced, data but it only show data from normal browsing.

There isn't; that's the point of private mode.

Nope. That's what Private is for, to prevent a trail.

If you don't save the private mode data, once you leave it is gone. So screen capture, email, share what you visit, make private mode habits, that allow you to save things you want saved. Otherwise deal with it all being wiped out when you close out private mode.