How is the 2015 Macbook Pro on Big Sur?

Sorry for parsing words but " I'm looking to update my 2015 MBP to 11.5.1" implies Big Sur is already installed and update to newer version of Big Sur.

Though if what is really meant is the upGrade to Big Sur - that changes this a bit.

Firstly - the age of the computer. MBP all the way back to Late 2013 can run Big Sur. The condition of the battery is also a factor. A computer from late 2013 with a battery of that age may not perform as well as a MBP from something newer.

So in general - if the computer qualifies for Big Sur it should work as intended. Just be sure to have a Rescue Plan in Place before attempting >> This comprises having 3 Backups using 2 methods and 1 Off Site incase of Theft, Loss or Natural Disasters. A Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS. For addition purposes - two Tested Bootable Clones each to separate external drives. This is insurance incase the upgrades goes sideways. At least one Tested Clone and / or Time Machine Backup should be Off - Site

I recommend updating your MacBook Pro to the latest version of macOS if it supports it. personally I'm using a M1 MacBook Air so I don't really know the performance increase your specific model will get. but it will help with the longevity of your MacBook.

Check if your MacBook Pro supports it here.

https://www.apple.com/macos/how-to-upgrade/

Have you checked your battery with an app like CoconutBattery? It can tell you a lot about the condition of your battery.

That way you'll know before upgrading to Big Sur if there's a possibility of a problem.

For additional reading before attempts

https://discussions.apple.com/docs/DOC-250003367