Ahh, my bad
You probably need root (via sudo )
However, it matters not since you have the partition information
I'm not sure that sda5 is 'recovery' since it is so small. It is probably diagnostics, health check things like memory, harddrive graphics and so on.
Options as I see them.
- use the free space as a single 'large' root (/) partition
Creating a swap file on that partition.
- delete sda5 and then let Mint set everything up
- delete everything, install windows, then mint
- add a new drive
To create a swap file
dd if=/dev/zero of=/swapfile bs=1000 count=2000000
echo "/swapfile none swap sw 0 0" >> /etc/fstab
That will create a 2gb swapfile ,
But this isn't ideal, distroa normally create a swap partition equal to the ram in size to take advantage of hibernate feature.. I'm not certain it works with a swapfile.. but never tried myself
Are the other options.. options?
See if you can boot the diagnostics, try f10, f11 , f12 during post (look for messages advising the 'key' to press on screen or in manual/support site.
Once in determine its 'usefulness'
If you do remove sda5 (and the logical partition ) you should be able to make new logical partition using available 'space' and then have multiple linux partitions
In any case, backup your data and have windows install media available, 'just in case'