I am currently aware of 3 operating systems being developed for the librem 5
1.Pureos (comes with phosh and plasma mobile as ui)
2.postmarketos
https://postmarketos.org
https://wiki.postmarketos.org/wiki/Purism_Librem5_Devkit_(purism-librem5dev)
3.ubports
https://ubports.com
Once the librem 5 will be mainlined I believe any gnu/linux os which can run on arm64 will run on the librem 5
Other linux based mobile operating systems I know are
4.Maemo leste (based on devuan)
https://maemo-leste.github.io
5. Luneos
https://www.webos-ports.org/wiki/Main_Page
Replicant os (based on android but fully free)
https://www.replicant.us
Memo mobile
https://wiki.merproject.org/wiki/Nemo
AFAIK Nowadays PureOS, PostmarketOS and Mobian are the OSes you can install on Librem5.
Aparently Mobian runs very well
Although collaboration with Ubuntu Touch was published, no progress is currently being made in that direction