I need to update my operating system. My Mac won't allow it. It is currently running on OS X Yosemite 10.10.5. I'm thinking I might not have enough memory to handle any operating system beyond Yosemite. Could this possibly be true?

It would help to know the exact model of the Mac which you can get by clicking the Apple menu and selecting "About This Mac".

What OS is it suggesting you upgrade to? There have been some reports that some computers are offered a version of macOS that is not compatible with their Mac. This article lists which Apple hardware is compatible with various versions of macOS:

https://eshop.macsales.com/guides/Mac_OS_X_Compatibility

Also, here is an Apple article which contains links to various macOS installers as well as instructions for creating a bootable macOS USB installer:

How to create a bootable installer for macOS - Apple Support

Many times third party apps such as an anti-virus software, cleaning apps, or third party security software will interfere with the normal operation of macOS and prevent an OS update/upgrade. You can try booting into Safe Mode to try the update/upgrade again. These types of apps are not needed on a Mac and usually causes more problems than they solve.

MLR2015 wrote:

I’m having same issue. Saying I need to update to run other software but it won’t let me.

Details matter. We have no clue what your system is. Is your Mac even compatible with a newer OS? Have you read my previous post and did you try those suggestions? I did provide several tips and articles for the OP which should also help you.

Writing an effective Apple Support Commun… - Apple Community

I’m having same issue. Saying I need to update to run other software but it won’t let me.

No; any model capable of Yosemite can run El Capitan.

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