Can I update OS on MacBook Pro (2010) from 10.10.5 to 10.11 or later?

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install.  For Best results use Safari to commence the download as Others may not work.

Safari will open a redirect and open the Apple Store where the download can commence.

macOS High Sierra 10.13 hardware requirements Reasonable certain High Steer is the last version this computer Qualifies to run

macOS Sierra 10.12 hardware requirements

OS X El Capitan - Technical Specifications

Make Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS

Yes, you can do that, check this article:

How to get old versions of macOS - Apple Support

Check this link find your Mac model

https://support.apple.com/en-us/HT211683