Sometimes the open driver works well, but it seems the hplip driver is more stable. The hplip driver for HP LaserJet P1005 needs a proprietary plugin, that you need to download first. This can be done via hplip-gui, but last time I tried I got an error stating that the checksum didn’t match for the downloaded plugin. The solution was then to:
* Uninstall the printer
* Purge and reinstall hplip (may have been unnessecary).
* Download the plugin from [openprinting.org](https://www.openprinting.org/download/printdriver/auxfiles/HP/plugins/).
* Download the file called 'hplip-x.xx.xx-plugin.run',
where you replace the x-s with the hplip installed version.
* Reinstall the printer with `sudo hp-setup`
* When asked for a plugin, choose the one you downloaded.
* The printer should make some noises, and should now work :)
Sources: