The trick to the puzzle is that the cards are marked. The wheel in the upper-left corner of each card tells you the number of the card, and the small circle mid-way up on the left side of each card tells you the suit.
The very last skywriting clue reads:
1:00=A ... SW=HEART
This is the "key" to reading the card markings. The wheel reads like a clock, with the 1 o'clock position signifying the Ace, the 2 o'clock the two, etc. The small circle tells the suit, depending on where the quarter-circle is placed. The south-west (lower left) means Hearts. The remaining suits have to be found through deduction.
So, the first card is the two of hearts.
The next card is a four. Since the only four is the four of diamonds, we now know that the north-west position signifies diamonds.
The third card is the six of hearts.
The fourth card is an Ace. The only two aces are the Ace of Spades and the Ace of Diamonds. Since the quarter-circle is not in the NW position, it cannot be a diamond, so it must be the Ace of Spades.
The final card is a five. Since the quarter-circle is in a new position and one of each other suit is already present, it must be a club, the five of clubs.
Clicking on each of the five cards in the upper row in order will reveal the true cards and enter the following into the "Submit" field:
2:H, 4:D, 6:H, A:S, 5:C
You can also simply enter the above into the field and hit "Submit."
To next puzzle: Tale of 2 Brothers.