MCU powered from the same PSU as a LED strip
Yes, you can do that, however bear in mind that if you make some programming error, and all LEDs are on the adapter might be ruined, so you might want to add some protection (fuse?), if not already protected. If the PSU does not have a fuse already, I would use a 5A fuse (same as the adapter itself). I also would advise not to use 5A continuosly by LEDs (and MCU), stay at e.g. 4A for have some margin.