why should the suction head of a pump not exceed 5psi?

Are you talking about the design requirement or the actual suction head? I have seen plenty of pumps with the actual suction head over 5 psi. Often, larger pressure centrifugal pumps, like boiler feed pumps, have much higher suction head because they are fed by either a condensate pump or a booster pump.

If you are attempting to require a suction pressure greater than 5 psi, you may not be able to get there because the water will form vapor in the eye of the impeller and cause cavitation. Cavitation occurs when the bubbles collapse in the higher pressure regions of the pump impeller forming a small implosion. It sounds like pumping rocks. It can damage the pump.

It depends very much on the design of the system that the pump is installed in and the design of the pump and its driver. You need to provide a great deal more information before anyone can give you a very good answer.

Note: I have seen pumps installed with suction pressure ranging from an almost full vacuum to well over 1000 psi. So pressure in its self is not a factor

A higher pressure should not cause cavitation. That is almost always due to lower pressure.

I assume that: Above 5 psi the water will turn to a vapor (cavitation) and the pump will burn up.