Controlling SMD-LEDs using a 74HC595 & NPN-transistor as switch
If you use NPN or n-channel MOSFETs your circuit will get much simpler. By raising the LED voltage supply you can put them in series reducing the number of resistors and the heat dissipated. Since the 74HC595 sinks and sources you can connect the gate of the mosfet directly to the 74HC595 output, the source to ground and the drain to the series string of LEDs. If you use a transistor yo will need to add a resistor to each base. Size the MOSFET or transistor to be able to supply all the current the LED string requires. More current capacity with the MOSFET will allow it to run cooler as the voltage drop across it will be less.