I have a mac air, on os 10.10.5, latest version according to this site, app store shows no updates? Any suggestions on what to do?

If your MacBook Air is 2012 or later (see Apple menu > About this Mac for that information), then see: How to upgrade to macOS Catalina - Apple Support

If it is earlier than 2012, please reply with the year.

Hi, 10.10.5 is as far as 120.05 can be Updated, you're looking for an Upgrade. :)

See if you can upgrade to 10.12, 10.13, 10.14, or 10.15, see sys requirements...

https://support.apple.com/kb/sp742?locale=en_US

https://itunes.apple.com/us/app/macos-sierra/id1127487414?ls=1&mt=12

https://support.apple.com/kb/sp765?locale=en_US

https://itunes.apple.com/app/macos-high-sierra/id1246284741?mt=12

https://support.apple.com/kb/SP777?locale=en_US

https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12

macOS Catalina - Technical Specifications



General Requirements

▪ OS X 10.9 or later

▪ 4GB of memory

▪ 12.5GB of available storage (OS X El Capitan 10.11.5 or later)*

▪ Some features require an Apple ID; terms apply.

▪ Some features require a compatible internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Catalina:

▪ MacBook (Early 2015 or newer)

▪ MacBook Air (Mid 2012 or newer)

▪ MacBook Pro (Mid 2012 or newer)

▪ Mac mini (Late 2012 or newer)

▪ iMac (Late 2012 or newer)

▪ iMac Pro (2017)

▪ Mac Pro (Late 2013 or newer)