Is FileVault enabled and if so has it finished Decrypting the drive Before attempting the update to 11.5. If Yes, try Disabling FileVault and allow it to finish. Then - suggestion below
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