This is not true for LCD monitors. LCD monitors are basically 'instant on' and therefore there is no state change for anything in the monitor and therefore almost no wear and tear from turning on and off.
Whoever sold you this was selling you "Whatever's new is perfect," and just like last decade's new stuff, it isn't.
LCDs operate with a backlight. It's a fluorescent light. Power cycles on a fluorescent light are:
1) What kills them.
2) The most inefficient thing you can do to them.
5 minutes is too aggressive, and you will absolutely end of life that bulb faster if you encourage a habit of turning it off while the user is using it, causing them to instantly turn it back on.
The result is an entire monitor with plastics and poisonous materials being put in the ground that will MORE than eliminate any small gains of saving a little electricity.
The ideal solution comes in 2 parts:
1) Be reasonable with power saving. 15 minutes for the monitor to turn off.
2) If you can, try to run a screensaver for a very short time before the power save kicks in. 10 seconds is ideal but Windows will probably only let you get down to one minute. This warns the user they're about to lose their image, and they'll shake the mouse then, without the backlight having to powercycle.
My favorite solution to this is on Ubuntu/Gnome, a version of Linux. After 15 minutes the screen slowly fades to black. If you let it keep going it goes all the way to black then the monitor turns off. Smooth transition and an obvious signal to the user that if they want to keep looking at what they're doing, shake now.