You seem to think that reorganizing your complete system while it is running is possible (you say “How can one change the current partition lay-out of a running Tumbleweed system?” and you try a partitioning tool from your desktop). This is not the case (like you can not change the tires of your car while driving).
So you need a (maybe called life/rescue system) booted from another medium then the disk you want to reorganize.
And be prepared that this is not that easy. The unallocated space that you want to add to partition 5 is before it and not contiguous at it’s end. Thus a lot of moving back and forward is involved. And a serious thought out plan should be made.
Whatever you decide to do in the end, make extra backups of everything before you start.