how do I increase the available space for this part of my harddrive?

This is the warning message by the wya

First of all: backup the user data!

The easiest solution is to reinstall. When the installer asks for the type of install, choose "Other" (or whatever it is called nowadays). Then, within the partition editor integrated with the installer, delete the existing partitions, recreate a larger partition (say 48 GB to be at ease) with a filesystem (ext4 is fine) to be mounted at /, a swap partition (as large as your RAM if you want to hibernate, otherwise smaller), and another partition, taking the rest of the disk, with a filesystem mounted at /home.

For that last filesystem, Trisquel chooses XFS by default. It is fine. In particular, XFS is efficient with large files, such as user files. But a drawback is that XFS cannot be shrunk. That is because I imagine your /home is on XFS that I suggest you to reinstall. Because you cannot shrink it, you would have to delete it, enlarge the root partition, recreate it, and edit /etc/fstab. All from a live system. You can try that though, if you want to learn.

Notice that you need not lose all the work you put into installing packages on top of the default system. See https://trisquel.info/en/wiki/cloning-system-or-how-make-copy-installed-packages-one-computer-another

$ sudo apt-get clean

Your /var tree is really heavy. What is using so many space there?

Moving system unencrypted tree (sda1) to encrypted volume (sda5) is not
simple.

El 20/10/19 a les 0:03, name at domain ha escrit:
> Hi,
>
> Trisquel gave me a warning that I was running out of space in a part of
> my  harddrive ... would you help me understand this?  How do I increase
> the  allocated space?
>
> This is soon after a fresh install with a new 500 gb SSD on which I
> installed  Trisquel, and a secondary platter harddrive of 750 gb.
>
> Screenshot attached
>

Or instead of encrypting the home directory encrypt the entire drive. Then you don't need to deal with / and /home being different partitions as they are showing in your screenshot and then potentially running low on space with one while the other might still have gobs and gobs of space left. That requires using the netinstall image which, last I checked, has been broken for about 8 months now. Welcome to Trisquel.

The /var directory consumes two thirds of the partition space. Try to clean it first.

When there is enough space on the / partition, then you can perform other optimizations.