Help with LED matrix

Hello,
I'm hand-building a 5x20 LED matrix and I would love to use my Arduino to drive it. Also I would like to keep extra components to a minimum. The problem is I need the matrix to be capable of fast animations so I'm not sure how to do the transmission. I was thinking of using parallel transmission with software MUXing and external DEMUXing and splitting the matrix into 4 or 5 slices.
Or if i decide to use shift registers and serial transmission will that be fast enough?

Question no 2: can I drive a 5x4 led matrix directly off arduino using only current limiting resistors? (I'm too lazy to do the math)

short answer

yes, but something will die rather quickly

can I drive a 5x4 led matrix directly off arduino using only current limiting resistors?

Even shorter answer :- No.

Look at how I did it:-
http://www.thebox.myzen.co.uk/Hardware/Mini_Monome.html

Also I would like to keep extra components to a minimum.

So do you think there is an engineer on this planet that says to himself "I know I don't need these components but i am going to put some in just to make it more expensive for some one else to make this design"
If a part is included it is (or should be) needed.
You can't source 20 or even 5 LEDs with the 30mA capability of an arduino pin. (don't use them at the absolute maximum of 40mA that is only a stress rating)