Simple Transistor Circuit Question
The 2nd circuit doesn't work because to turn on the transistor you need a base emitter voltage of 0.7 volts and that means, at best the emitter is at about 4.3 volts and that would be the voltage on the relay.

Think about the first circuit and why it works - it's easy to forward bias the base emitter junction because the emitter is at ground. With the emitter connected to the relay, the moment you apply the base voltage the emitter must rise with that base voltage but be 0.7 volts lower. This only partially turns on the transistor.

Or if you expected the emitter to be 12 volts in the 2nd example then the base would need to be 12.7 volts.

The bottom line is that the forward biased base emitter junction IS a diode and behaves like one.