- make sure you shutdown and do not suspend or hibernate
- if the battery drains when the system is shutdown this is a -hardware- related problem. Not of the operating system
powertop
and any software will need the operating system to be running yes.
- 5% could be what it costs you to boot your system.
- check if it is actually draining: is it 10% after you did not use the system for a week for instance? If it is always 5% ... I do not call that "draining when powered off".
How can I troubleshoot this?
Not from inside the operating system.
edit: check that USB is turned off. Maybe your BIOS is keeping an USB 3.0 port active (one that can be used to charge something while the system is down). Maybe go through your BIOS?
Is there any way to conduct a software check on the battery health? (although new laptop)
Example:
How to check battery status using terminal?