Why NPN switch doesn't have voltage?
From what I understand, 1V on base should be enough to make
  collector-emitter basically a short circuit, so there should be 5V on
  resistor. What am I doing wrong?


1 volt between base and emitter usually turns on the transistor reasonably well (but beware of putting too much current into the base). 

The trouble is with an emitter follower (like your circuit) is that as soon as the transistor starts to conduct, the emitter voltage rises and cuts down the base-emitter voltage hence, the emitter can never rise higher than what is applied to the base. 

But it's a bit worse than that because you need anything between 0.5 volts and 1 volts to make a decent base current and that means the emitter voltage must be about 0.7 volts lower than the base voltage AND if you apply 1 volt to the base, the emitter might only reach 300 mV.

The above applies to NPN transistors and, with some thought also to PNP transistors.