You can use gparted to move & resize your partitions. If you're going to be working on your root partition ie. "mounted at /" you'll need to make a livecd or bootable usb drive to boot into gparted.
More info can be found in this guide.
Edit: Now that your image link is working, I can be a little more clear. If you were to shrink and move to the right your sda5
partition that will add to the amount of unallocated space between sda7
and sda5
.
Being that you're going to be working on your root parition, you'll need to do it from a gparted live usb.
Once you've shrunk sda5
to the right, you can drag the boundary of sda7
to the right, using that unallocated space to make it bigger.