it was a long time ago but I think I did install the software first, however I have since reinstalled (clean install) windows, the mouse and keyboard were working before I re-installed the software.
I would install it the way Logitech says, you can uninstall the software later in settings, if you wish, the drivers will remain.
"My old Microsoft Wireless 5000 is showing it's age and the wheel acts up sometimes. Could be since the big dongle is plugged into the back of the pc. "
you could try an extension lead to bring the dongle onto the desk to see if there is any improvement but sounds like its getting worn out.