Service Unavailable after WP update

Hi,
during the last week I got email message informing about automatic updates of all four WP sites managed by me (to 5.2.4 or 5.1.3 respectively). Since this update I can’t access these site any more and getting the Service Unavailable message instead. In various internet sites plug-ins or themes are blamed for this error but as I did not change any of them I wonder what caused the trouble and how to deal with it.
Any hint is highly welcome.

Mixay