FYI, the adapter pictured won't help you get from your 3/8" thread to 5/8". That particular set of adapters is to take you from a 5/8" stud to a 5/8" thread (and also supports 3/8" thread as well, I think).
We know your Shure bar is threaded 5/8"-27. You need to find out exactly which thread/stud size your stand/clamp is to ensure you get the proper adapter.