Powering LED strip and Raspberry Pi from a single 10A 5.5V power supply
raspberry pi is designed to run off USB power which is 4.75 volts to 5.25V
a Schottky diode (eg:1N5817) will give a 0.3 to 0.4 volt drop which should do what you ask. 

However I'd be concerned about the compliance of the power supply, how stable is that power supply voltage under load, and under supply fluctuations.  it might make more sense to employ a cheap buck-boost (SEPIC) DC-DC converter to supply the raspberry pi.