Simple tutorial -
1. Download a ROM for your Nexus 5, any stable one is fine.
2. Make sure you have downloaded all the needed files for the ROM you are going to flash.
3. Boot your N5 into recovery mode and plug in your USB cable.
4. Make sure you have adb tools on your PC. If not, download the adb tools from Google. Or you can get it when you download the SDK.
5. Move the ROM you have just downloaded to your desktop. And the extra files if there is any.
6. Open cmd and link it to your adb folder. ie - cd c:/path/to/adb/folder
7. Inside the cmd window, push the rom.zip file to your device like this. adb push /path/to/desktop/rom.zip /sdcard
8. Do the same thing with the extra files you have downloaded, if there is any.
9. Once transfered, in recovery mode. Simply wipe data and cache. Then flash the rom. Reboot your device.
10. Have some hot cocoa because you just fixed your Nexus 5.