If you circuit needs 6V to operate from 4AA batteries and can't operate on 5V then you need a boost converter to generate 6V from the 5V supply. (No need for an LDO).
But try the circuit first to see if operates okay on 5V.
Four AA cells are 6.4V when brand new and are 4V when they need to be replaced. Surely the circuit still works when the battery is 5V which is no where near being dead.