Nope. Katesimon's idea wont work.
You've got a level shifting problem - The PNP digit drivers bases need a drive signal referenced to the 5V rail, but your logic signal swings between 0V and 3.3V. The difference between 3.3V and 5V is 1.7V, still plenty enough to turn the transistors hard on. If you are *cheap* you can get semi-acceptable level shifting from your circuit by carefully choosing the base resistors to form a potential divider so Vbe is small enough not to turn the transistors on significantly when the MCU digit output is at 3.3V, and also so Ib is high enough for saturation when the output is at 0V.
Try R11=390R and R10=1K2, which will give you an on state forced beta of about 20 @Ic=30mA, reasonable for saturation, and an off state Ic that should be under 1uA at 25 deg C.
The down-side is that even when off, the MCU output must sink approx 1mA at 3.3V, and this may be problematic as you'll have 1mA * Ndigits trying to pull your 3.3V rail upwards when all digits are off. If the minimum load on your 3.3V rail is insufficient, adding a 3K3 pulldown on each digit output from the MCU should solve that with negligible effect on the other parameters. Alternatively if you are really cheap, omit the pulldowns and add a load resistor on your 3.3V rail!
LTspice sim attached.