I'm not using a 5K iMac, but it might not be a Lightroom problem. If you're still sending images up to your Wordpress site at 670 pixels and 72 ppi, you're exporting photos that are perfect...for your old, non-Retina screens. Retina displays range from 218–227 ppi on the Retina Macs to 326–401 ppi on the latest iPhones, so if you're still basing your pixel dimensions on 72 ppi that's not anywhere close to what you need. They will seem pixelated next to the higher resolution text and graphics around them.
For a website to look good on a Retina display it should have what are called "2x" assets, in other words double the pixel dimensions across and down. If your old standard was 670 pixels across, for Retina displays the site needs images 1340 pixels across to be as sharp as the rest of the page.
(that's just a guide I found quickly using Google; there might be better links out there)
I also resent the same pics through the same process on my old Mac and they were perfect.
Just to be make sure we're going down the right road, are you saying the images exported from your old iMac looked perfect in Wordpress on both iMacs, or looked perfect in Wordpress only on the old iMac?
Thank you Conrad! I bet that's it. I can't check tonight but will tomorrow. Thanks a bunch
And make sure you're running Wordpress on a server with ImageMagick enabled, else you will loose sharpness while Wordpress resizes your images: Wordpress forgets to sharpen images after resizing (which is always required of course).
I wrote a plugin for that: Plugin: Sharpen your photos on WordPress with ImageMagick - Hans van Eijsden Photography
It also checks if your webserver has ImageMagick enabled.