I was wondering how many years should a pair of studio monitors last. Is there a rule of thumb where every 5 to 10 years you should replace them. Thanks

Good question, I suppose if you use them all of the time then periodically when you can hear their performance is deteriorating.
 

depends on whether or not you are talking about powered monitors, vs passive monitors.
 

Like a fine wine, I say...better with age.  If they're taken care of, they should last well past 5-10 years although it would depend on the quality of the product as well.
 
I've had my passive Event 20/20's for nearly 20 years.  Been tempted to go powered but why....they sound great!  I had a set of JBL L20's (albeit home component speakers) for nearly 30+ years and I loved them like the day I bought them.  Did have to replace the foam on one of the woofers at around 24 years but they kept on keeping on.

I've had a pair of Advent Model 1 speakers since 1976. I treat them with respect and they still sound great. The surrounds have been replaced twice because UV light breaks down the foam. As long as they don't deteriorate mechanically, they could last for decades. Cross over components like capacitors should likely be changed every 10 years if they drift with age.

My Event PS8s have been with me since '00 or '01 or there about.

Lolol, I have the passive Event 20/20s as well from 2001 and last year upgraded my amp from a QSC MX700 to a Crown XLS 1502. Apparently they can last until they blow up it sounds like :) .

How funny!  I ran them for a long time on an Alesis RA100 till I picked up a used Hafler TA1600.  Like I said, I've been tempted over the years mostly by the Yamaha HS series but just couldn't justify the expense for what I do and know that I would have seller's remorse.
 
I'm sure that technology continues to improve and there certainly might be improvement on sound quality but one just needs to weigh the expense, time involved in learning them, and to what extent you rely on them for what one does.
 
My latest temptation was on Sweetwater's latest special on 48 months 0% interest. I was eyeing and researching the Genelec 8030 LSE Triple Play 5" package.  Genelec's & no interest - woohoo!  Proud of myself for resisting!
 

Replacing monitors because they're X years old? That's crazy talk.
 
People replace their monitors because over the years speakers and amps have gotten better, not because the old ones wore out. Most commonly-used studio monitors from 20+ years ago weren't designed specifically for that purpose, but had been re-purposed from the worlds of hi-fi or broadcasting.  Nowadays, if you spend a little money you get what's essentially a scientifically-engineered piece of laboratory test equipment that's vastly superior to anything you'd have found in a vintage studio. (Whether or not that'll result in better recordings is another subject entirely. :)

It's worth replacing the speaker cones periodically if you use them a lot (more often if you play loud). This because no matter what you do, they lose some stiffness over time. I wouldn't replace the entire monitor though, especially not if they're active.

And by "periodically" I mean like maybe once a year with really intensive use but perhaps once every 10 years with more casual use. I don't believe many speaker cones (that get used) last much longer than that without losing accuracy.