To resize (shrink) the encrypted /dev/sda5 partition I have tried these steps:
-
Open a terminal in the live boot system
-
Open the encrypted partition using your LUKS password:
sudo cryptsetup luksOpen /dev/sda5 cryptdisk -
Then you’ll be prompted to enter the decryption key
-
After successful decryption you have root access to your now decrypted partition
-
Run
gpartedas root from the terminal and use the GUI to resize the partition
Step 5 does fail because “resize” of /dev/sda5 did not offer smaller partition sized.
Any ideas?
PS: I guess shrinking from within PureOS is not possible because the partition must be unmounted.
Update 1:
I have found step-by-step instructions how to shrink your LUKS/LVM partition:
https://help.ubuntu.com/community/ResizeEncryptedPartitions
It is so complicated and risky that I do understand now why Ubuntu recommends to backup and re-install 
If you still try to do so, I have some helpful commands for the first part (still incomplete):
# Load decryption kernel module
sudo modprobe dm-crypt
# Recognize and activate your LVM
sudo vgscan --mknodes
sudo vgchange -ay
# 2 logical volume(s) in volume group "crypt" now active
sudo lvscan
# Shows the two active devices within LVM (swap + root)
# /dev/crypt/swap
# /dev/crypt/root # this device is what we need!
# You could mount the encrypted partition now but DON'T DO this since it prevents resizing!
# mkdir /media/sda5
# sudo mount /dev/crypt/root /media/sda5
# Check the file system for errors before resizing
sudo e2fsck -f /dev/crypt/root
# Resize: Shrink to 70 GB (or whatever you want by changing the number)
sudo resize2fs -p /dev/crypt/root 70G
# Check that the file system is still OK
sudo e2fsck -f /dev/crypt/root
The next parts are still missing
- Reduce the size of your root (LVM) Logical Volume.
- Resize your (LVM) Physical Volume.