A FET would do the job admirably. Current is well within the capability of a PCB if you make the tracks wide enough. You could easily get up to 20A - 30A on and off a PCB without any unusual tricks and with enough effort PCBs can carry much higher currents. Think about your average variable speed drive for example - mains voltages and tens of amps on a PCB.
 

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If we learn from our mistakes I'm getting a great education!

Just find a FET with a lower R_ds  to avoid all temp issues.

Keith Cress
Flamin Systems, Inc.- http://www.flaminsystems.com

You can always just run fatter traces.  We've purchased laser diode drivers that can dump 200 amps direct;y from a single DFET.  Current came off the board through a 1-in wide flex cable.

TTFN

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Hi.  Agreed with that said before.  With a 1/2" track, you can route 10Amps with some 4ºC temp rise.

Use a FET rated well over your 5V/10A, and saturation Vgs near 5V.  You will likely use those TO220 cases, so you can lay it down horizontal over a huge copper island to use the same board as heat radiator, though most power FETs stay fairly cool with high currents.

Be careful with noise at the gate pin, you may want to add a pull down resistor of some 1Meg (N-Channel FET), to avoid false triggering while the micro is powering up, as the control pin of the MCU will be likely tristated.

Good luck with your board!

Regards,
Gonzalo

For high currents like this it is usual to specify 2oz copper rather than the usual 1oz. This halves the track resistance.