Will 5V Trigger a 12V Relay

Advanced Member level 5. You cannot activate a 12Vdc relay with 5V.

How many volts does it take to trigger a relay?

Most are rated at 12v, usually a range of 12-15v. Actual voltage required to operate the relay is usually a little under 12v. That is why your accessories can still operate with the key on and engine off, usually making actual voltage a bit under 12v with lights on.

How much current is needed to trigger a relay?

The relay draws 40 mA at 5V applied directly across it. It is the current required by the relay to operate. Your calculation of 40 mA is correct.