Digital LED clock - matrix circuit question
Since you're using a matrix of anodes and cathodes you need to connect/disconnect both ends of each LED. 

You will probably multiplex these LEDs and only light one at a time. Are the LEDs high enough current that you can't either source or sink enough current for a single LED directly from Arduino pins? Most LEDs run on ≤ 20 mA, which an atmega328 can handle.

If you are trying to drive LEDs that need > 20mA then your plan to switch both the +5 and the ground with transistors should work. As StarCat said, you should consider the "on resistance" of your transistors as part of your calculation for the value needed for the current limiting resistors of your LEDs.