Here are some really basic questions. I'm sure you went through them with Amazon, but if you could tell us the answers it might help figure out what's going on.
1. Has it ever updated itself via wi-fi or download before, or is 5.12.4 the software it came with?
2. Are you sure you have a basic Kindle and not a Paperwhite? Go to device info and look at the serial number. Does it start with either G0910L or G0910WH? If not, look up your actual model here:
https://www.androidauthority.com/whi...-have-1073996/
3. Did you download the right software? This is the link for the basic Kindle update:
https://www.amazon.com/update_Kindle_10th_Gen. The file name is update_kindle_10th_5.13.5.bin. If you have anything else, you may have grabbed the Oasis or Paperwhite software by mistake.
4. Why do you want to upgrade? Is there some other problem you're trying to solve?