Auto-protecting power sources with no voltage drop
Rather than approaching the issue from the point of view of the assumed solution, here is an alternative, and extensively used solution:

Use a point-of-load switching regulator to supply the desired 5 Volt supply to the target device (your microcontroller board), sourcing the supply for the regulator from whatever upstream voltage source is available. 

Any number of voltage sources can be hooked to the regulator using diodes, one per source line. 

By using an auto-switching buck-boost regulator, great flexibility is obtained in upstream  voltage options, while maintaining the target 5 Volt output from the regulator. This particular example supports adjustable output from  1.25 to 35 volts, with input ranging from 5 to 30 Volts, with a current rating of 4 Amperes.

Here is a simplified schematic for the specific application requirements stated in the question:







simulate this circuit &ndash; Schematic created using CircuitLab