Yes, all 2950's support two processors.  An OS reinstall is also not necessary.  Both processors MUST match EXACTLY.  So, if you want to use your existing E5405 processor, then the second processor must also be an E5405.  The E5405 comes in two "stepping" versions:  E0 and C0 ... the stepping versions must also match.  It would be strongly recommended to update the BIOS and ESM before the upgrade though.
Is it possible to add another processor to a Dell PowerEdge 2950 server?  The server was built in February of 2005 and came with a single Intel Xeon E5405 CPU. I will be installing ESXi 5.1 on the server and changing the RAID configuration, so nothing needs to be retained software-wise.  
Dell PE2950 - Can I add second CPU?