Here's some calculations using the air-standard tables.
For five pounds of boost: If you have a "ACME-100" perfectly adiabatic compressor it will require 11.24 BTU of energy to increase the pressure of one pound of air by five psi from ambient temperature (80 deg F) and pressure (14.7 psi). The temperature of the air as it leaves the compressor will be 127 degs F.
Unfortunately, all the "ACME-100" compressors have been recalled, and the best compressor you will be likely to find -- at least for automotive purposes -- will only be 80% efficient. The amount of work to pressurize the same amount of air will be 14.05 BTU, and the resultant temperature will be 138 deg F. The increased temperature is the result of the inefficiency of the compressor. It takes part of the mechanical energy and converts it into heat energy.
If you use a Roots type supercharger, the efficiency will only be about 50%. The resulting compressor work is 22.48 BTU per pound of air, and the discharge temperature of the air is 174 degress F.
To put this into perspective, consider a six liter (350 ci) engine with a volumetric efficiency of 90% that is turning at 3000 rpm with the throttle wide open. That engine will use about 23 pounds of air per minute. If a supercharger is used with 5 psi of boost, the air mass will increase to about 31 pounds/minute. The amount of power required for an 80% efficient compressor will be about 10.3 hp; for the Roots supercharger with an efficiency of 50%, 16.4 hp will be required for supercharging purposes.
Now let's look at the numbers for 15 pounds of boost. The mythical 100% efficient adiabatic compressor will require 28 BTU of energy for each pound of air compressed by 15 psi. The post compressor temperature will be 200 deg F. An 80% efficient compressor will require 36 BTU per pound of air, and the discharge temperature jumps to 230 deg F. The roots compressor takes 57.6 BTU, and the exit air is at a temperature of 322 deg F.
Looking at our six liter engine, the air flow through the engine is now increased to 46.7 lbs/min (assuming a 100% efficient aftercooler, but that's another story. . .). A 80% efficient compressor takes 39.7 hp, while a Roots supercharger will require about 63.5 hp.
Well, I'm getting tired of typing. If anybody wants, I will quantify the amount of heat removed by an aftercooler and how much aftercooling decreases engine work and thereby increases engine output.