How to select the center frequency and filter type for 5-band digital audio equalizer?
The answer may depend on your application. I suggest you look at some commercial audio equipments with EQs to decide for those band frequencies. For example the old analog philips casette-type stereo system in my room has 5 band graph equalizers with the frequencies: [100-300-1000-4000-10000] Hz respectively. I use it as an amplifier for my laptop :)

If you design the first and last bands as Bass/treble shelve types, be careful to limit their cutoffs so that mid bands will have enough spectral intervals.