5V@5A switching power supply shuts down after few seconds
Apparently you have already found the cause, which was that you had long cables from the power supply to the load, which caused excessive voltage drop whent the load started drawing significant power.  You have worked around the problem, but not really fixed it.

Shorter cables is a good idea, but just cranking up the voltage so that you still get the minimum at the load under maximum current conditions is not a good solution.  That could possibly cause over-voltage at other times.  The real problem is that the voltage is being regulated at the power supply, not at the load which is at the other end of the cables.

Look at your power supply more closely.  It probably has sense inputs.  These are for exactly your case.  A separate wire is used to feed the actual voltage at the load back to the power supply, and sometimes the same with the ground.  These wires are only signals and carry little current, so don't have any significant voltage drop accross them.  They tell the supply what the voltage is where you actually want the voltage regulated, as apposed to what it is at the supply.  The supply then adjusts its ouput (within some limits) to be whatever is needed to produce the correct voltage at the load.