External monitor turns off for several seconds every 5-10 minutes

If your screen is switching off it might be struggling to keep sync with the output signal.

There are two main reasons for this , the first is refresh rates being too high for the screen to keep up with and the second is the cables are not good enough. There is an outside chance your graphics card can't cope with multiple screens but most are powerful enough.

Which connection method are you using and what resolution are the screens set to ?

Xrandr will allow you set and query the refresh rates. Sometimes knocking a few hz off the frequency can work around bad cables.

If you have other cables you can borrow try them.

you xorg logs (in /var/log/ but check the dates of the files) should show the resync attempts and shed some light as well

The same has been happening to me intermittently over several months. I use Ubuntu 16.04 and have a Dell Latitude-E7440. There seems to be a pattern here with laptops! Mine seems to be due to the battery not charing properly and the Energy settings getting changed some how. I ran this to turn the Energy features off.

$ ~ xset -dpms

This resolved my screen turning off randomly.