How do I add an empty partition to another disk for more space?

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You can simply add the /dev/sda5 partition to your existing volume group on /dev/sda7.

You can do this as root:

At this point the command pvs should show a single physical volume on partition /dev/sda7

Get to know you LVM structure with the commands vgs and lvs. You should see a single volume group and some logical volumes

First you make the partition /dev/sda5 into a LVM physical volume. Make sure that this is the correct partition and it does not have any data on it and it is not mounted anywhere. Any data on /dev/sda5 will be lost after this command:

pvcreate /dev/sda5

Since the partition is not empty, you might have to --force it: pvcreate --force /dev/sda5

Now you can check that pvs shows two physical volumes, one with a volume groupe on it and one without an associated volume group (/dev/sda5)

Take a note of the volume group name shown by pvs

Now you just add the new physical volume to the existing volume group:

vgextend NAME /dev/sda5

Now use the commands pvs, vgs and lvs to see how the situation has changed.

Now you can extend you existing logical volumes and the file systems on them using these instructions

Personally I'd purge all of Windows garbage (5 partitions, but not EFI one), maybe unless there was some cool diagnostic utility (doubtful).

If you ever need to reinstall windows, your license is stored in BIOS and on MS servers. Fresh win ISO's are now officially available for download (with recovery you'd install back all of Lenovo bloatware).

Other then growing and/or appending another logical volume (@jmt's answer) you could also move your Linux partitions to the beginning of the disk (where disk should perform better) with e.g. gparted or even start fresh:

1. save list of installed packages dnf history userinstalled > installed-pkgs,
2. backup your /home with rsync,
3. format entire disk, reinstall Fedora, restore /home and reinstall packages.