How do I update my software from 10.9.5 to the latest version?

Not knowing your hardware the safest option is to download the install creator for OS X El Capitan 10.11 using a direct download link to start:

https://support.apple.com/en-us/HT206886

The link for El Capitan is one of the links in Step No. 4 of that document. You double-click the download .dmg disk image file to see the "package" file contained inside, and then run the package which creates the Install 10.11 El Capitan "App" in your Applications folder. You can then run that App to upgrade to 10.11.

Once you're working on El Capitan (which, crucially, updates your version of the App store) that opens further upgrades via the App Store if your hardware is compatible. From 10.11, you can reliably do a direct-upgrade to any version your hardware is compatible with and not have to upgrade one version at a time.

For example the next (possible) upgrade to consider would be 10.13 High Sierra using the direct-app-store upgrade link in Step No 4 of this other document:

https://support.apple.com/en-us/HT208969

(10.13 High Sierra)

Or here:

https://support.apple.com/en-us/HT210190

(10.14 Mojave)

Both documents also have 10.15 Catalina upgrade links, again, it depends on your hardware compatibility. You can further check your hardware compatibility here:

https://support.apple.com/en-us/HT210222