OK, I can now see the pictures...
marcusbarnet, the VCCIO pin of the FT232RL chip is the supply voltage input for the serial input and output pins. The FT232RL is bus-powered from USB (VCC, 5 volts) and generates its own 3.3 volt supply from that (3V3OUT). If you check the datasheet for the FT232RL you'll see that it can work with VCCIO in the range 1.8 - 5 V.
In the version of this board now being supplied there are three solder pads which are connected to 3V3OUT, VCCIO, and VCC. As supplied, VCCIO is bridged to 3V3OUT so the I/O pins will run at 3.3 V. If you want them to work at 5 V, unsolder the bridge from VCCIO to 3V3OUT and solder VCCIO to the VCC pad instead. You don't need to supply the 5 V from your own regulator, and if you don't want to use the 3.3 V supply then don't connect anything to 3V3OUT.
Or, if you want to leave yourself the option, unsolder the 3V3OUT bridge and then use a wire on your breadboard (as shown in the first picture) to connect VCCIO to your chosen I/O supply voltage.
Hope that helps!