Is using a 12.5V PSU ok for a 12V LED? Also would this wiring work?
Ok,

No, this will not work.  Right now your strip's + is connected to ground, the most that would happen is that the strips power connections would both be grounded.  But even worse is the simple fact that your switches have NO ground connection, so turning them on would have no effect.

I edit this shortly with a diagram showing how to fix it, DONE.







simulate this circuit &ndash; Schematic created using CircuitLab

With a 250 resistor your going to get about 28 mA. The way to calculate is below.
Finding the value of the resistor is easy once you know what the strips current requirements are.  

Here I'm going to use 30mA as the required current.
First determine how much voltage that the resistor will need to drop.
12V(source) - 5V(required) = 7V
Now we solve for resistance(ohms) by dividing the voltage(in volts) by the current(in amps): R = V/I = 12/.03 = 233 Ohms.
The resistor will have to handle watts = V x I = 7 x .03 = .21 watts, I would bump that to half a watt.  This will require either a single 1210 240 ohm, or 5 0605/0805 47 ohm resistors in series to handle the 1/2 watt that will be dissipated in the resistor.