I had a very vague thought. I was wondering if I could I create a dual power supply using an Arduino uno and a nano. Can the ground terminals of both the boards be shorted and the 5 volt terminals be used as +5v and -5v . Is this possible? Would it damage the board??
No, because both 5V terminals are +5V.
If both boards are powered by completely isolated power supplies then you could connect the +5V of one to GND on the other. One will then have all its signals and logic negative to your ground level, but normal compared to its own ground level. Managing it though and keeping things separate (no shared ground between two sets of peripherals, etc), would be tricky. And the moment you plug one into your computer the whole lot could go up in smoke.