Probably nothing will happen. Because if you get a link from such websites, they already have thousands upon thousands of backlinks and your 5k won't make any difference![]()
Why you thinking about ranking??
Look at the bigger picture...you try to rank to get traffic. If your link is prominent on a major new publication, the traffic will drive itself. If you are able to do this, then spend less time backlinking and more time getting your links on more publications.