OK, so I was a stupid boy and TIFU.

Yes, you can take as long as you need to get a game for a winner. There are no actual penalties for having "not received" games on you profile.

you can always request permission to delete the giveaway, can never force them to accept though(even in the groups with it as rules, they will just get removed and blocked from those groups if they don't approve it.

It's not like you're tarred and feathered for an invalid key. As you gave away well hung keys the developer might have revoked them. A despicable practice which is not reigned in by Steam. An understanding winner would consent to delete the giveaway although they don't have to according to SG rules.

I believe your winner would need to mark it as 'not received' to be eligible for other GAs of the same title, so don't bear any ill-will to the winner who does that.

Note, in the 5-week scenario, it's possible your winner gets the key from some other source (another GA, a trade) in that time, and then they'd be less likely to mark it as 'received' from you. If they got it from another GA, marking it as 'received' in your GA would earn them the mark of being a multiple-key winner.

As with most problems, sincerity and communication should go a long way toward finding a solution that satisfies both sides.

The winner himself proposed to delete the giveaway. Should I use the reason "Gift or Key no longer available" the other option named "Accident" or another one?

What others have said. Remember that for each non-received mark, you lose one giveaway slot, which isn't good if you want to make large trains in the future. I always try to make an agreement to delete the giveaway and most users are understanding on these situations.

Totally off-topic, una amiga con su pareja han pasado el finde en Navarra, no sé dónde narices han ido pero que todo precioso, me han dado un poco de envidia. Que suerte tenemos los que vivimos en el Norte Verde, verdad? Saludines desde cerquita de Bilbo.