You cant hook it up in series because LEDs have a certain forward voltage, to get current to flow through the LED you need to apply a voltage higher than that (here is a diagram of the voltage-current characterstics for different colours http://www.telatomic.com/images/electricity/pepc5.jpg
If you take that a white LED drops about 3volts of voltage, and if you were to wire two of them in series you'd need a supply voltage of at least 6 volts to get them to light up. As your supply is only 5 volts you can't really do much here (other than getting into various voltage booster circuits like the joule theif)
You also can't wire all the LEDs in parallel and use just one resistor, each component has slightly different tolerances and the LEDs with slightly less voltage drop will shine brighter than the ones with higher voltages and such.
Using only a potentiometer to do the dimming is a viable option for your setup, however each LED would still need its own resistor to limit the maximum current. Try a couple of hundred ohms in series with the whole series/parallel array.
The issue with potentiometers is that wanted to dim a higher load, the amount of waste heat in the potentiometer would quickly go over its rated power.