There are hybrids of the various suggestions as well, e.g. multiplex the LEDs as a 7x5 matrix, use a shift register for the 7 columns, and drive the rows via MCU pins.
Populate the entire 7x5 matrix, add a real time clock, and with a little extra code, the thing could be laid out like a calendar and work fine from year to year. Not sure if that's the look you're after though, and I'd probably explore simpler solutions first 
Merry Christmas! (Now that's really rushing the season isn't it!)