You can use even 1S battery if you use DC-DC upconverter like NCP1402SN50T1G and you'll get 5V from it. Just make sure that your converter of choiсe can handle the current. Or you can use a linear low dropout voltage regulator like MC33269 to get 5V from 2S battery (or more series batteries) but I wouldn't recommend using more than 2S battery since the conversion efficiency will reduce. When choosing a linear regulator, make sure it accepts voltages down to 7.2V since minimum voltage a single li-ion battery can give is 3.6V and (again) that it meets your current consumption requirements. And don't forget the heatsink if you're planning to power something like RPi.
Now I see, you need maximum battery life. In that case, you'll need maximum conversion efficiency. Maximum efficiency can be reached with properly chosen DC-DC converter, so your question narrows down to whether use a step up or step down converter (1S or 2S battery respectively). In general, step-down converters are more efficient than step-up but would you give up the ease of 1S charging and handling for a few percents of efficiency? LTC3441 or TPS63002 converters, for example, can reach 92-93% efficiency in step-up mode if your device draws 300-500 mA, it's a very good performance.