Can a late-2013 Mac desktop (2.7 GHz Intel Core i5, 8 GB memory) currently running OS X El Capitan 10.11.6 be upgraded to a newer OS?

Your Late-2013 Mac Desktop (aka iMac) can upgrade as far as macOS Catalina (10.15.7). If you have 32-bit applications that cannot be upgraded by their vendor, or by your need for their functionality, then you might want to only upgrade to Mojave (10.14.6) as it is the last operating system to support 32-bit applications.

I suggest that you obtain the free Go64 application to determine what 32-bit applications that you currently have, and whether their vendors now offer 64-bit versions of them. Also, before you upgrade the operating system, ensure that your printer/scanner vendors have compatible drivers on their website(s) that support the upgrade operating system.

Before you upgrade, perform a Time Machine backup of your El Capitan operating system, and then using exclusively the Safari browser, visit How to get old versions of macOS for the link to your upgrade choice in the App Store. The installer will be in your /Applications folder when the download is complete.