You can do the Win keys (also known as GUI keys) in two ways, both of which are "normal" keys (versus multimedia/consumer control keys).
One is to report them as up/down using bits in the modifier byte of the key report, the other is to send the codes like regular keys. In the latter case it's 0xE3 or 0xE7. Both methods seem to be widely supported. If you are using them as modifiers you need to keep them down while you add in the second key. Also make sure your HID report is standard enough to support those codes (that is don't set you max value lower than E3).
So the process for a modifier would be to report the Win key code. Then report the Win key code plus whatever it's modifying (like Win+A for instance). Then report the Win code. Then report all zeroes. If you just want the Win key by itself just skip the report with the A key.
0xE05B is wrong, that sounds like a PS/2 code.
GB