Z80B very hot with slow clock?
The Z80B is an NMOS chip so it draws full current continuously. Maximum specified current draw for the Z80B is 200mA, corresponding to 1W at 5V. It normally runs hot.

Though the NMOS Z80 is a static design, the maximum specified clock low time is 2us. If you use a slow clock it should be arranged to pulse low for no more than 2us, and remain high for the rest of the time. This can easily be done with a 555 timer, using the Discharge pin to set the low pulse width. Clock high level must be close to 5V, so use a pullup resistor with the 555, or use the CMOS 7555.   

You should have decoupling capacitors valued at 0.1~1uF as close as possible to the power supply pins of all digital ICs to absorb spikes caused by logic transitions, and a larger capacitor (eg. 10uF) across the supply input to smooth out lower frequency voltage variations.  

The address lines can only source ~250uA and sink ~2mA, so you should use 'super-bright' LEDs with high value resistors to avoid loading the outputs. Alternatively you could add buffer gates to drive the LEDs at higher current.