Powering a 5v relay from a 12v power supply
Your relay is rated for 5 V and you know its DC resistance is 400 &Omega;.  That means it draws (5 V)/(400 &Omega;) = 12.5 mA.

Yes, a resistor would work to drive this relay from 12 V.  The resistor needs to drop 7 V with 12.5 mA going thru it.  From Ohms law it needs to be (7 V)/(12.5 mA) = 560 &Omega;.  Your calculation is therefore correct.

You should also consider the power dissipation of the resistor.  It will be (7 V)(12.5 mA) = 85 mW.  That's within what a "&frac18; W" resistor can handle, like something in a 0805 case.

Yes, that's about all there is to it.