The CAT4137 is a switching driver. It will boost the input voltage to light the 5 LEDs when placed in series. It's a bit more complex of a circuit with the inductor and schottky diode being something most people don't have on hand, but it'll do what you want.
If you're worried about the varying voltage from the LiPo, why not just monitor the battery voltage with the Arduino and adjust output appropriately?