You have a few options, but I would not recommend several of them for a new user.
First, the 68 GB unallocated space is not part of
sda5 is now just under 1 GB. You might be able to delete
sda5, thereby increasing the size of the unallocated space by 993 MB. But the question is why
sda5 is the way it is.
If you simply chose to make it that size or were unsure if you could delete it and chose to just make it small, you can probably go ahead and delete it. But...if when you shrank the partition,
gparted would not let you make it any smaller, trust
gparted and leave it alone.
Keep in mind that you will need to perform any actions from live media, since you will not be able to work on a logical partition without unmounting the logical partitions with a higher number.
Option 1) Move
sda6 to the left and then resize it to to fill the space.
This is not recommended for a beginner. Moving a partition can cause data loss, can take an extremely long time, and will almost certainly leave the computer unbootable into either OS until you reinstall
Option 2) Make an new
ext4 partition in the unallocated space, move the contents of
sda6 into it, and then delete
sda6 and increase the size of the new partion.
This is also not recommended for a beginner, but is arguably better than Option (1). For instructions, see Move the whole installed files to another partition. If you are interested, be sure you understand the steps before doing anything. Note that it will also render the computer unbootable until you reinstall
Option 3) Use the live media to do a clean install into the unallocated space.
For a beginner, this is the easiest and safest thing to do. You can make a new
ext4 partition either during the install or before.
I would recommend backing up all of your data to external media. Then using Try Ubuntu, then use
gparted to create an
ext4 logical partition in the unallocated space. Give it an easily recognizable label, like NewInstall.
After that, run the installer, choosing the Something else option so you can specify the partition you want.
Then move your data to the new install and reinstall your packages and programs. This step might be time consuming, but IMO it is much simpler for a beginner than trying the other options.
Once you are satisfied that the new install is correct and that your data are safe, delete what is currently
sda6 (be careful since the numbering may change) and resize your new partition into that space.
Menus for deleting, creating, or resizing partitions are found in
gparted by right clicking the partition or using the Partition menu.
Option 4) Deleting the swap partition, expand
sda6 into that space, and create a swap partition in the unallocated space.
This is generally safe, but is problematic for a couple of reasons.
a) You have filled 50 out of 52 GB already. I would guess that either you have a lot of data or have installed a lot of packages. In either case, I doubt the extra 7 GB will be enough and you will find yourself in the same position before too long.
b) Deleting the current swap space will require changes to your
fstab file. Again, this is not recommended for a beginner.