Switch 15V source with a MOS by digital 0/5V (dc)
You have an N channel MOSFET connected as a source follower. A source follower (just like an emitter follower for BJTs) can't have as it's output a voltage any higher than what is put on the gate. In fact, for a MOSFET, the source voltage will be a couple of volts less than what is on the gate - this is why you see 3V. The act of connecting your load to the source ensures that you cannot achieve full-turn-on unless the gate rises higher than 17 or 18 volts from ground. But all is not lost....

Ask yourself - what turns the FET on - answer - the gate to source voltage has to be a couple of volts or even higher on some fets. This can only mean that the fet is partially turned on.

You ought to consider grounding the source and putting the train lights in the drain. Like this: -



Rd is where you'd connect the lights. Now with the mosfet gate at 5V with respect to grounded source the fet turns on much better.

Another way is to use a P ch MOSFET driven from a BJT: -



Because the P channel FET's source is up to the positive supply, pulling the gate down to GND ensures it turns on to the lowest resistance. Don't run this circuit any higher than about 15 volts though because the maximum FET gate voltage might be limited to 15 volts - read the data sheets - a lot of mosfets are OK for +/-20 volts gate-source but some are only rated at max 12 volts.