Definitely NOT the site's software, Gerry.
If it were the software, there would be errors stating something like, 'The Data Base Is Currently Unavailable', or some such which are usually NOT in the 500 error range
500 errors are typically server end errors.
In the worse case scenario, it could be a server denial attack and in the 'best' case scenario, their servers are inadequate for handling the 'normal' expected load.
An upgrade and/or expansion of the servers would likely resolve the later.
Updating 'denial attack detection' on the servers and/or rebooting the servers MIGHT
solve the first.
FYI: One of my sites was hit with a 'server denial attack' awhile ago. It took less than 2-hours, after the first complaint was posted, for the hosting service to bring all of the sites (100's of them) back on line and to apply additional security measures to prevent future server attacks.
Since I was also confronted with both the 500 and 503 errors today, and such seem to be intermittent, I would tend to lean towards the inadequate server scenario here, rather than a full-out sever attack. That's the good thing, though it may take longer to fully resolve the problem for everyone due to internal/external server/local page caching as it may take some time for the cached error message pages to be replaced (refreshed) with the current 'live' pages on the server(s).
Though it is a major inconvenience. I would NOT expect it to continue for months, or years, as has been the case in the past. (fingers crossed)