Older Shimano 105 Pedal question

Happy t giving all -- I wonder if any of you can help me. My bike is about 12 years old -- a specialized epic allez -- and has shimano 105 pedals that were originally set up for use with a cage and strap -- the cage and straps have been taken off at some time and are missing in action.

So, in looking at Shimano 105 pedals on-line now, they look nothing like these. Does anyone remember or know what shoe/cleat system these might be compatible with?

Or have things changed enough I'd be better off getting all new pedals?

Thanks in advance.......