There are 3 ways to open the Mystery box
1. By watching advertisements. You need to watch a certain amount of advertisements in order to open the box. The progress is shown above the button. If you stop watching an advertisement then the counter will save the last successfully watched advertisement. However, if you restart the game the counter will be reset. When the counter is fully filled - the box will be opened.
2. By Mythical coupons. You can acquire them as a reward for the end of the season or receive them in event chests.
3. Gems.
Also, you can open the box 5 times in a row, however, this offer has a limited count per day. If the window with x5 offer doesn't appear, it means that limit has been reached. Now you will be able to open the box 5 times in a row only on the next day.