Big Sur 11.5 : Download failed . Please check your internet connection and try again.

Welcome and Thank you too :-))

Regarding " Other " Category and not good news. Source of below https://support.apple.com/en-ca/guide/system-information/syspf9b375b9/11.0/mac/11.0

• Other: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

Yes Available Empty Space would be and could be a Major Issue. Just like the upgrade from previous versions of macOS to Big Sur - Apple clearly stated require 36 GB of empty Space.

A similar requirements is for the update from Big Sur 11.3.1 or 11.4 to 11.5. The installer requires empty space to download, expand and install.

Bood practice is the Always keep at least 15 GB Empty Space Available at ALL Times.

If this update is for Big Sur 11.5 - the error message can be misleading. There are factors like poor Wifi connection, slow wifi connection, too many other people downloading at the same time and Apple Severs are overloaded, Software on the computer interfering with the download process, running behind a VPN and or / if via wifi too many Other devices using the wifi at the same time reducing the Bandwidth to you computer.

There are several ways to download the Big Sur 11.5 update. 

1 - Connect to Router via Ethernet connection and restart the computer in Safe Mode and then open the Apple Apps Store and get the Full Installer of Big Sur. It will be the 11.5 version and once downloaded run the installer from the Applications folder.

2 - Resart the computer in Recovery Mode ( INTEL Command + r ) and choose Reinstall macOS. It too will download the full Installer and commence the installation. For M1 CPU the Recovery Mode is Here

3 - This method may seem unnecessary but sometimes the Router Restart clears Network issues from ISP to Apple Servers

Shutdown Router. Shutdown computer and disconnect all External Drives. Restart Router. Connect to Router via Ethernet Cable. If via Wifi - Disconnect all other Devices using the Wifi - want the Maximum Bandwidth only for this computer. Restart computer in  Safe Mode. It does a Repair Disk, Clear System Cache files and only load Apple Software, extensions and Fonts. Will load slowly - Normal. Once Logged in - open Apple Apps Store and  Get the Full Version of Big Sur. It will take some time and several pauses will occur - normal. Countdown clock may say 15 minutes but in Real time may be 30 minutes. Same goes for clock at 10 minutes could be 20 minutes in Real time. Eventually , Full Installer will download and a New Application in Applications Folder will present called Install Big Sur. Stop there and perform a Time Machine Backup. If desired - have an External Drive - Copy & Paste the Install Big Sur Application to external drive for future usage - making a Bootable Installer. Now run the Installer.

Have found this method more reliable than the Software Update which is very iffy at best

Are there any AntiVirus, Disk Cleaner, Optimizers, Defrag, VPNs etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS and may even Corrupt the OS requiring a Reinstallation.

I suggest that you need to pay attention to the message you received. If it says that the download failed, it is because something occurred during the download which corrupted the file. Therefore it can not be installed. I'll bet that you used Wi-Fi to do the download. It is generally too slow for these very large files and corruption may occur. If you did use Wi-Fi, I recommend that you use a wired Ethernet connection for OS updates and upgrades. Do another download. That will usually resolve the problem. If storage capacity were the problem, you would have been so notified. Let us know what happens. If the problem continues, then we can look more closely at internet issues.

Sorry, but that solution doesn't fit Apple's model. My MacBook Air has no ethernet port, which implies Apple expects people to use WiFi. As long as the network is fast, the download should work. BTW, I'm experiencing the same problem. Previous big upgrades have proved problematic for me as well. I suspect the issue is at Apple's end. The techs would by now be aware of the situation. Previously the problem took a few days to solve, so I'm going to be a little patient and wait for the fix.

Have you got enough space in your disk to install and download Big Sur?

I had the same error message and I realised I hadn't enough space.

I freed some space and worked!