@Tom – I think you may have customized your Emoji & Symbols keyboard shortcut somewhere along the line – I also have a system with OS X 10.10.5 also and the shortcut is command-control-space. I’m sure I’ve seen command-control-space listed in some tips & tricks articles also, so I’m pretty sure that is the standard.
It was far back in the mysts of time when I set up the Hide/Show Toolbar menu, so I couldn’t remember how it got that shortcut. Looking at most other programs, they either don’t have a Hide/Show Toolbar menu item (you have to use the popup) or if they do, no shortcut. But then I discovered that Keynote, Pages and Numbers DO all have this menu command and they use the command-option-T shortcut. So Apple is where I got that! (Those programs do have that item in the View menu though, rather than the Window menu.) I don’t think I actually got it from Keynote, Pages and Numbers though – I think XCode set that up automatically for me when I first created the Panorama X project file.