Can I update my old macbook Pro (mid 2010) OS X 10.9.5 ?

A Mid 2010 MacBook Pro can run up to Mac OS 10.13 "High Sierra."

You can get High Sierra here:

How to upgrade to macOS High Sierra - Apple Support

NOTE: Others have recommended only using Safari to download the software. FireFox users are apparenty having issues with macOS download links.

You can go up to MacOS 10.13 High Sierra with a mid-2010 MBP. So yes, you can update to 10.9.5 if you want...or higher.

Time Machine is a complete backup, I’d use that.