Monthly Puzzle #6 [ENDED][SOLUTION INSIDE]

Hello again and welcome to another puzzle. Solve it for a chance to win:

• Dragon's Dogma: Dark Arisen (US/CAN)
• Astrea: Six-Sided Oracles
• Dream Tactics
• Heretics Fork
• Intravenous
• ...and a bunch of other cool stuff!

In case you're new to puzzles, usually the objective is to obtain the unique 5 characters code of a private giveaway:
https://www.steamgifts.com/giveaway/XXXXX/

Find the code consisting of three letters and two numbers. Each character is used just once.

1. F5D4k One letter is correct and well placed. One number is correct and well placed
2. x7J1F One letter is correct but misplaced. One number is correct but misplaced
3. L75Ga One letter is correct but misplaced. One number is correct but misplaced
4. t31JP One letter is correct but misplaced. One number is correct and well placed
5. 4FtL2 Nothing here is correct

Solution

Lets find the code consisting of three letters and two numbers. Each character is repeated once.

Let's start with Clue #5, and delete all the incorrect characters from the other clues.

1. -5D-k One letter is correct and well placed, one number is correct and well placed
2. x7J1- One letter is correct but misplaced. One number is correct but misplaced
3. -75Ga One letter is correct but misplaced. One number is correct but misplaced
4. -31JP One letter is correct but misplaced. One number is correct and well placed

Clue #1
We now know that one letter between D and k is correct, and we already found one of the correct numbers, and its correct placement:
?5??? D/k

Clue #2
Either x or J is correct, and either 1 or 7 is correct.
?5??? D/k x/J 1/7

Clue #3
Either a or G is correct.
Either 7 or 5 is correct. But we already know from from Clue #1 that 5 is correct, which means that 7 is wrong.
But according to Clue #2 only one between 1 and 7 is correct, this means that the only other correct number is 1.
We found all the numbers. Let's focus on positioning later. We still need to confirm three missing letters.
?5??? D/k x/J a/G (1)

Clue #4
One letter between J and P is correct.
One number between 1 and 3 is correct and well placed. We already confirmed that the correct number is 1, so now we also know its position.
?51?? D/k x/J a/G J/P

Let's focus on the letters. We're now left with these four options, and no more clues:
D/k a/G x/J J/P
We know we must find only three letters, and that's why we can determine that J is of these three. Not simply because it's a repeated option in two clues, but because any other choice would leave us with four possible available letters.
This is how we determine that J must be one of the three letters we're looking for.
?51?? D/k a/G (J)

Going back to Clue #1, either D or k is the right letter, in the correct position. But the third character, where the letter D would be,
is already taken by the number 1, which leaves us with the letter k, in the fifth spot.
?51?k a/G (J)

Going back to Clue #4, we know the correct letter is J, but we also know it's misplaced, so it doesn't belong in the fourth spot.
The only other free spot for this letter is the first one.
J51?k a/G

Going back to Clue #3, either a or G is the right letter, in the wrong position.
If G was the right letter, it would contradict the hint about the position, since the only spot left is the fourth, which leaves us with the letter a as our only possibility.
At this point you could also bruteforce the last character, but as you can see, it can still be found with facts and logic.

J51ak