Basically it sounds like you went to indoc and then quit while waiting for the call back for systems. Which means you should have received the 5k initial check. In this case repayment is in the agreement you signed, I think it's full repayment if you leave before a year and pro-rated for the year after that. How legally binding that is I don't know, there's quite a few threads discussing whether airlines can force repayment of signing bonuses.
However, if you never received the 5k bonus check you need to talk to the recruiting department asap to get things cleared up and a stop payment on that check, as they are under the impression that you cashed it.
Sorry if the details of this are a bit off, the numbers have changed since I went through.