Hi I am running a OS X version 10.9.5 on my imac. software it says is up to date. how do I upgrade to a newer os system?

you cannot upgrade directly from mavericks to big sur.

first you need to upgrade to el capitan. click here>> OS X El Capitan 10.11

then you will be able to upgrade to big sur. click here>> Get macOS Big Sur

A 2014 iMac can run the latest macOS

see > https://support.apple.com/en-us/HT211683

Be aware that if you upgrade past 10.14 "Mojave," most of your older apps will not work. Mojave was the last OS to run legacy 32-bit apps, like old versions of Adobe Creative Suite/Cloud and any version of MS Office older than Office 2016.

IF you upgrade to 10.15 Catalina or macOS 11 Big Sur, your will need to first see if thei developers developed 64-bit updates of their 32-bit apps you use. If they do not, you will have to repurchase or find a different app to do the same tasks. Many classic Mac games were never converted to 64-bit. They will be unusable.

To find what 32-bit apps you have, this tool is helpful:

https://www.stclairsoft.com/Go64/

You can get the same information from the System Information utility on your Mac but the report is more cluttered and and harder to read.

What year model is your iMac?

see > https://support.apple.com/en-us/HT201634

Try one of the older macOS's like El Capitan or High Sierra first.