Manufactures of computer monitors say that they should last from 50,000 hours to 60,000 hours of usage and at 8 hours of use per day the monitor should last between 18 to 19 years easily.
However that is for the led bulbs etc but other things in the monitor could fail sooner than that.
I have a 12 year old Dell Computer monitor that is still going strong and an HP computer monitor that is 8 years old and although it's getting a little dim it's still works fine.
Usually you'll be replacing your computer itself before replacing the computer monitor due to it failing.
Dust, cockroaches and other bugs can shorten the lifespan of your computer monitor so keep your computer monitor cleaned and keep any roaches or bugs away from the computer monitor and it should last easily a decade or sometimes more.