27K seems way too high for driving a 7SEG display. if you are using 5V, than 1K should give you 3mA also driving current, which is safe for 7SEG and certainly is fine with MAX7219. Since your display is rather large, it might still be a bit dim at 3mA and you can try using a 500 resistor if that is the case.
There are 5 LEDs per segment in a row - darn!
On page 12 of the max7219 is a MAX394 used for this problem.But would a ULN2803 work also with all the common cathodes? It's easier for me to get than the MAX394 and it doesn't need -5V