The 6 instead of 5 might be also due to be "a little over 5", so 6. As you said, it doesn't really matter if its 5.5 or 6. They might just rounded up.you do not change that value. with open loop (R3=infinity) OpAmp gain is huge. but adding resistors constraints that gain to some lower, fixed value.
this is how gain is calculated:
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gain in image 22 (p6 of datasheet) is 5 because:
a) this is noninverting amp (signal is on input+)
b) resistor ratio is 2000Ohm/500 Ohm = 4 so total gain is A= 1+4=5
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in the project you linked, gain is controlled by ratio of resistors R3 and R4. their ratio is 600/120=5 so overal gain is 1+5=6 (and not 5), likely just a typo. And after all, this is just an audio amp so gain 5 or 6 makes little difference. If this was an instrumentation circuit, such difference in gain would be catastrophic but in audio applications you have a volume knob and adjust it as you please. so of the signal is too high (for whatever is after this stage) you can choose to reduce R3. if it is too low and you need more gain, you can increase R3. if you want to follow that project as is, stick with the R3 value they used. buffer is just buffer so it an be ignored since gain = 1. rest of the parts in the feedback loop (R1,C1,C1a,R2,C2) are shaping frequency response.
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