After 5 minutes, for example, if not plugged in.

It is most always plugged in and this just started a day or two back.

The sleep settings can be such that ... even when it is plugged in .. it will blank the display.

Check your settings in System Preferences / Energy Saver (or Battery) panel and review the "Turn off Display" settings.

Also check your "hot corner" settings. The four corners can be set to sleep or turn off the display. These settings are under "Hot Corners..." in the "Screen Saver" section of the "Desktop & Screen Saver" panel in System Preferences.

Screen saver
Energy Saver

settings could use slight modification as a test. Settings can get lost, so the small test is a start

Reset PRAM and SMC. You may have something acting up in how power is being controlled for sleep/wake, assuming it’s not just a purely physical issue that’s sending the wrong signal.

I nearly always find the same issues.

That wears out prematurely and that somehow causes the screen to go out and come on. I dunno.

I have a 2016 macbook touchbar 13" and one month after the 1 year warranty I noticed this "stage lights" issue. 5 months later the issue is worse now.

Yesterday, I noticed that when I tilt the screen back beyond the 90 degree angle the screen goes black. Then if I move it back to 90 degrees it gets illuminated. But the angles vary a lot. Sometimes it gets illuminated only If I move it back to 60 degrees and sometimes a little more than 90 degrees.

Apple appears to have a run of displays failing in the new 2016/17 models!

Sadly, the cable between the backlight within the display and the connection to the logic board is the issue here. The flexing of the display (opening & closing the lid) fatigues the wires within the ribbon cable. The complete lid needs to be swapped out.