This isn't a bug, it's a misunderstanding about what "positive question record" means. This is somewhat confusing, so you're not alone! It does not mean that the five questions you asked must have a positive score. It means that we count your total questions and subtract questions that are somehow "bad", including deleted ones.
The formula for this is:
(total questions - negative questions - closed - deleted)/total questions >= 0.5
Yes, a question that is closed, deleted and downvoted counts against you three times. Even if you were aware of this formula, it can be somewhat difficult to figure out your record for yourself if you have deleted questions that you're unaware of or forgot about - which you do.
You have 27 total questions of which 4 are closed, 15 deleted and 1 has a negative score.
(27 - 4 - 15 - 1) / 27 = (27 - 20) / 27 = 7/27 = 0.26
0.26 is less than 0.5 so you do not have a positive question record.
Note that deleted questions, in particular, are a real problem for your record! If you don't need to delete a question - don't!
If you figure the answer out yourself, write an answer so that the community can benefit. If your question doesn't get an answer, that's OK. Having unanswered questions gives others something to solve; there may be a solution, eventually. There are, certainly, times that a question can't be fixed and should be deleted but that's generally a signal to slow down and double check things before asking.
You even deleted an answered question, which means you're preventing the person who took the time to answer for you from benefiting the site. This includes duplicate questions. Something being a duplicate doesn't mean that it can't be useful to others.
If you don't undelete any of your questions and you don't have any more closed, downvoted or deleted, you'll get the badge when you have asked 40 questions.