I have a Dell Multicolor Laser Printer E525w. Its firmware is a few versions old; in particular I'm wanting Version 01.04.07, A05 (page: dell.com/support/home/us/en/04/Drivers/DriversDetails?driverId=NC1WV )
According to the page there is only Windows driver-installers available (even though the update is solely for MacOS issues, ironically.)
Other things I tried, to no avail:
(a) Checked that my printer's menus suggest it has "firmware update downloads' enabled:
Menu > System > Admin Menu > Secure Settings > Software Download > Enable
(This was the existing setting, and it's been connected to the internet for months.)
(b) download the driver .exe, move it to USB, and insert into printer;
(c) As above, but extract the .exe into a folder before inserting into printer via USB
Btw, the whole reason I'm looking for the firmware update is that the printer seems to often not respond to wireless print-requests, and I have to turn it off/on for every print job.