1 - When Bryan initially picked one of the 10 boxes, his chances were: 1/10 and the chances of the other 9 boxes were: 1/10 for each box.
2 - When Carl opens 5 empty boxes, the chances of your box is still 1/10 but the chances of the remaining boxes suddenly jumped to 1/5 for each box including yours.
3 - So, if you keep your original box, your chances are still 1/10 because you picked it out of 10 boxes. But, Carl is giving you the chance to increase your chances from 1/10 or 10% to 1/5 or 20%. Therefore, you should switch your original box to one of remaining 4 boxes, therby doubling your chances of winning the gold coin, from 10% to 20%.