You can find a very useful information how to replace a broken Olympus C-5050 mode dial at http://myolympus.org/5050/modedial/
I've found another way to fix the broken mode dial in C-5050 with a small plastic bolt even without disassembling the camera - it took me just about an hour to fix the camera. I've bought a thinnest plastic bolt 6x30 I could find at Lowe's, then I've drilled a hole in the dial ring a bit wider than bolt diameter and then made existing hole in the camera body a little wider but smaller than bolt diameter. Be careful with that - do it just turning the bit by hand. Don't enlarge the hole in the plastic ring with electrical contacts - you'll be able to screw the bolt into existing hole.
You can see all the steps on attached photos.
The fixed mode dial works great for me. The only problem - I don't feel nice old flicks for the dial positions anymore, but I can live with that. I love that camera and blame Olympus mechanic designers. In a similar way I fixed the broken battery door on the same camera. I've screwed it to the thick body frame with small steel bolt which has convenient plastic knob - also bought it at Lowe's.
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