Root partition size remains same after partition resize with gparted

It looks like gparted did extend the partition but not the file system. You will have to do that manually (ext4fs can be extended on a running system, even the / system).

Open a terminal and type

sudo resize2fs /dev/sda5

You will see something like "online-resize necessary" and then (after a few seconds) "the new size is ....".

Check the result with df -h once more - you should see the new size.