The description makes it obvious, and you will get this when trying to fill in a full month for other achievements. The only gotcha here is you have to actually play for 5 days, not go through 5 days of challenges in a single sitting.
Gimme 5! G20:
Play the Daily Challenge 5 days in a row
As of when i post this. You can do 1 challenge of the previous 5 days including the current day, in the daily challenges via the calendar all at once and it should unlock the achievement.
This can also be done with the marathon achievement.