It will depend on the voltage you are feeding the board. If you are giving it (say) 15V DC, the regulator needs to drop 10V (15Vin - 5Vout = 10V drop).
Measure the current the WC board is taking now and add your 300mA. Eg, if its now taking 200mA then add 300mA = 500mA total.
Power dissipation = 0.5A * 10V = 5W. It should be ok for a few seconds. Just make sure you put a decent freewheeling diode across the coil, otherwise the inductive spike it produces when you turn it off could easily kill things!
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