External Monitor not detected after upgrade to Mojave 10.14.5
I've hit the same wall with both my old and new Mac Minis when I upgraded to 10.14.5 this week. They're both ok with the HDMI cable to the monitor (so at least one is useable), but don't play nice with the HDMI/VGA adaptor/cable that I've also used to enable a second feed to the screen. 

Screen sharing between them is the only workaround, and I note this an issue with Mojave that pre-dates 10.14.5 (such as here https://discussions.apple.com/thread/8625812 and here https://forums.macrumors.com/threads/no-signal-on-external-displays-after-mojave-update-2018.2128056/).