The whole prop could be divided into fifths, so you'd only need to texture 1/5 of the circle. I'd probably just eye ball it, then adjust it back and forth until it looked right.. For the patterns that go in a circle, I'd make a tileable and unwrap that strip in a straight line so that it wraps in a circle.
I've always wondered how people draw circular shapes like the one on the top of this table. The problem is that the circle should be divided in segments and software should support some visible guides to help with that. Is there anything like this in PS, Illustrator, Inkscape?