I know the pin looks small compared to the cable you'd run to a wall socket for a 10A current - but those cables are a lot longer these copper pins, and cables

I know the pin looks small compared to the cable you'd run to a wall socket for a 10A current - but those cables are a lot longer these copper pins, and cables are sized with the assumption the copper will be coated in insulation then coated in another layer of insulation then installed into a wall full of insulation. A 10mm copper pin measuring 0.6mm x 0.6mm pin would have half a milliohm of resistance. Even if you ran your entire 5A load through a single pin, it would only have to dissipate 13 milliwatts. I'd be more worried about the PCB traces if I were you - 2oz copper is only 0.07mm thick :)