To earn this achievement, you must complete the daily challenge on 5 sequential days. Playing previous days does not count; you must complete the daily challenge as the days happen. If you miss a day, your 5 day streak will reset.
When I tested this today, I did not receive credit when I failed the daily challenge. In fact, I failed it twice and didn't get credit either time. However, I have confirmed that you can get credit for completing the challenge on the 2nd/3rd try, so take as many tries as you need.
Based on feedback in the comments: Changing the date on your device to a day in the past will break any existing streak you have going. You would then need to build a new streak by either changing the date and completing 5 consecutive past days, or by returning the device date to the current date, and starting over from scratch.