because the 8 pins only output 5v I would only be able to light about 8 LEDs at a time this way, correct?
No with 8 pins you could light 128 LEDs. 7 pins to define what LED and 1 pin to say if it is on or off. See addressable latches, these can control 8 LEDs but you can cascade 16 of them using two multiplexers to give you 128 addressable latches.
Use two 74LS153s to give you one of 16 data select lines to enable the 16 74LS259s.
But as I said before :- With a shift register you get to go to an unlimited number simply by cascading them. Use 74LS595, one for every 8 outputs you need.