Ah...OK. No, there is not going to be a problem with higher currents because these high currents will not flow through the Arduino GND, but instead back to the track power supply. Electrons will come through your "yellow" wire, through the MOSFET, then back to the "circuit" through the black wire. The GND connection to the Arduino will not carry any significant current (just the one to turn the MOSFET's on and off).
What your diagram does not show, however, is how you are going to power the Arduino. That power supply and its GND connection can also make a difference.
If you put this 5A circuitry on a PCB you will have to be a bit careful. I suggest 40mil traces to keep temperature rise 50C above ambient or less (the board will get pretty hot in those areas but nothing should be damaged at 25C+50C --> 75C). Or you can use 2oz copper (more expensive PCB manufacture) to use thinner traces or run cooler. Or run traces in parallel on top and bottom sides, or as you say, just use wires instead of traces. A common thing for people to do in the past was run solder on top of the traces to give them lots of thickness so they can carry lots of current. You can't do that if the board has a soldermask on the traces, but you can design it so the soldermask is exposed (or get a cheap board with no soldermask at all -- in which case you should tin it to avoid oxidation).
The Basic Motor Driver: simple, inexpensive motor driver for 1 stepper motor or 2 DC motors