It seems that Blizzard has been listening to its fan-base. On August 5 they announced that there would be a a change in the way rewards are distributed in Hearthstone. Now, you will receive rewards at the end of the season based on your highest rank achieved.
When you open your quest log, you will see something similar to the picture below. This will show the highest rank you have achieved over the season.
The rewards from the chest are given at the end and are based on your maximum rank. However, the cap for rewards is at rank 5. This means the only incentive to push above rank 5 is for the card back you receive.
The rewards from a rank 5 can look something like this:
These rewards begin this season, but will not appear in your quest log until around the launch of The Grand Tournament. The highest rank you have achieved will be retrospective, meaning it will include the rank you have reached before it is visible. You know what that means: it is time to begin the climb. Good luck on your laddering!