[Bender]

- Have you switched to a console screen vs X (control+alt+F1) to see if its actually X that is hanging and not the OS? Hanging 5 to 10 mins after using fdisk sounds like a red herring. If you are able to do this check dmesg. Just type dmesg. Then tac /var/log/Xorg.0.log | less

- Do you have sys-rq enabled and if so does the system respond to an emergency sync then emergency dismount then emergency reboot? [0] sysctl kernel.sysrq

- If you switch to run level 2 does this still occur? [1]

- Is there anything interesting in syslog messages in /var/log? Most notably Xorg.0.log and messages

- Do you have lm-sensors installed to watch temperature? sensors | grep -Ei ^temp Also check the temp of your drives smartctl -x /dev/sda | grep -Ei ^temp assuming your drive is sda. OpenIPMI can also get this data and fan speeds. If its hot do you have a dog or cat or something else that sheds hair? If so you may have to power it off, remove battery, open it up, use non metallic attachment on vacuum to remove hair, then compressed air, then vacuum again with non metallic attachment.

That would be my starting point. It could go a million directions from there.

[0] - https://en.wikipedia.org/wiki/Magic_SysRq_key

[1] - https://www.tecmint.com/change-runlevels-targets-in-systemd/