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For std Red LEDs forward voltage drop of 2V is typical. So min. 10V should lit up the LEDs to full brightness. Since you're not controlling the brightness a current limiting R should be used.
The PNP transistor is going to need a pullup on its base to LED + power. You also can't drive it directly from a 5V logic you'll need a open collector driver like a NPN transistor.
With 5 LEDs lets say White LEDs, so 5x3.1V+2x0.7V = 16.9V you'll also want it slightly higher so you can add a current limiting resistor so lets say 20V
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