Can I update iMac 27-inch with 3.5 GHz Intel Core i7 processor

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install. Make sure to use Only Safari to commence the download as Others may not work

Make a Time Machine Backup Before attempting. Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina and Big Sur Only support 64 bit and there is no workaround.

Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS and may even Corrupt the OS requiring a Reinstallation

Does your Mac meet these requirements?

These Mac models are compatible with macOS Big Sur:

• MacBook introduced in 2015 or later

• MacBook Air introduced in 2013 or later

• MacBook Pro introduced in late 2013 or later

• Mac mini introduced in 2014 or later

• iMac introduced in 2014 or later

• iMac Pro

• Mac Pro introduced in 2013 or later

To find the details about your Mac model, click the Apple icon  at the top left of your screen and choose About This Mac. 

EDIT -

macOS Big Sur - Technical Specifications:

https://support.apple.com/kb/sp833?locale=en_US