are shimano 105 st-5500 9speed or 10speed.
 

I've heard that they can accommodate doubles and triples, but can they also be used on a 10speed cassette? how about a mix of rear ultegra rd-6500?

Thanks!

They're 9 speed specific. If you want 10-speed you'll need the st-5600.

My understanding is that any SIS RD can work with any matching SIS compatible shifter/cassette combo. for instance 6-10 speed. as long as the shifter and cassette match one another, the RD will handle it fine. I've had very good luck using 8 speed rear derailers in 9 speed systems. and older SIS derailers with everything from 6-8. The exception is 6-8 speed dura ace stuff which was different from SIS.

Agreed. See this page by Sheldon Brown (of course).