Switching a Power BJT
The gain is pretty miserable on that high voltage BJT- the Vce(sat) is rated at a forced beta of only 5, and if you look at Figure 6, that's not unreasonable considering how bad the 'typical' performance is even at room temperature. So with a 5A collector current you would need 1A base current, which is above the capability of the 2N3904. If you used two of the HV transistors your overall gain will only be 25, so you'd still need 200mA. Not very practical. 

To look at it another way, you are giving the base of the output BJT about 4mA so it's good for switching about 5x that or 20mA. 

Even a modest logic level MOSFET will do much, much better than this if you are really switching just 5V. The BJT may be somewhat more competitive if you are switching hundreds of volts.