congrats man but I would have fought for that remaining 5k. If that was indeed what was discussed, and that was the amount you interviewed for, that should be the amount paid in the signing bonus (paid well over 15k to compensate for loss wages discussed below).
5k means a lot more to an individual vs a rounding error for a company, i call absolute bs they cant find this funding. Secondly, you didn’t just miss out on 5k, you missed out on end of year bonus (if it is a percentage of your salary), inflation increases yoy as a percent of salary, and 15k+ every year thereon out. You can do a simple calc to realize the TV you are being screwed. I’m very skeptical when it comes to outside recruiters, or recruiters in general, but I’d venture to say that head hunter just pocketed the difference (likely a nice bonus too given the aforementioned).
If i were in your seat, I would thank the recruiter for moving in the right direction but make it known she let you down and still owes you and that the issue is bigger than just a remaining 5k. Gl man